C Count cubes in cubic lattice cut by sphere around origin
C A cube with an inscribed sphere is divided into n*n*n
C smaller cubes. The program counts how many of the small
C cubes are cut or touched at their vertices.
C Cubes only touched by the cutting sphere, but all points
C either inside or outside the sphere are counted only half,
C because they occur in inside/outside pairs.
C Author: Hugo Pfoertner http://www.pfoertner.org/
C 16.07.2003
C
      IMPLICIT INTEGER (A-Z)
      PARAMETER (M=100)
      DO 100 R = 2,M
      RR = R * R
C L counts cubes fully cut
      L = 0
C N counts cubes touched at one of its vertices
      N = 0
C Loops over lattice points
      DO 110 I = -R, R-2, 2
      II = I*I
      IPP = (I+2)*(I+2)
      DO 120 J = -R, R-2, 2
      JJ = J*J
      JPP = (J+2)*(J+2)
      DO 130 K = -R, R-2, 2
      KK = K*K
      KPP = (K+2)*(K+2)
C Differences of squared radii of 8 vertices from cutting sphere
      D1 = II  + JJ  + KK  - RR
      D2 = II  + JPP + KK  - RR
      D3 = IPP + JJ  + KK  - RR
      D4 = IPP + JPP + KK  - RR
      D5 = II  + JJ  + KPP - RR
      D6 = II  + JPP + KPP - RR
      D7 = IPP + JJ  + KPP - RR
      D8 = IPP + JPP + KPP - RR
C      WRITE(*,*)R,I,J,D1,D2,D3,D4
      MI = MIN (D1,D2,D3,D4,D5,D6,D7,D8)
      MA = MAX (D1,D2,D3,D4,D5,D6,D7,D8)
C Check if sign change of squared differences occurs
      IF ( MI * MA .LE. 0 ) THEN
        IF ( MI * MA .EQ. 0 ) THEN
C Vertex hit
          N = N + 1
        ELSE
C Cube cut
          L = L + 1
        ENDIF
C      ELSE
      ENDIF
130   CONTINUE
120   CONTINUE
110   CONTINUE
C Only half of the vertex hits are counted
      WRITE (*,*) R, L + N/2
100   CONTINUE
      END
C Results: N       N_cut
           2           8
           3          26
           4          56
           5          98
           6         152
           7         194
           8         272
           9         362
          10         440
          11         530
          12         656
          13         746
          14         872
          15        1034
          16        1160
          17        1298
          18        1496
          19        1658
          20        1856
          21        1994
          22        2240
          23        2450
          24        2624
          25        2906
          26        3128
          27        3362
          28        3656
          29        3890
          30        4208
          31        4442
          32        4760
          33        5090
          34        5360
          35        5714
          36        6032
          37        6362
          38        6752
          39        7106
          40        7496
          41        7826
          42        8216
          43        8618
          44        9080
          45        9458
          46        9896
          47       10298
          48       10736
          49       11258
          50       11696
          51       12194
          52       12680
          53       13130
          54       13712
          55       14090
          56       14696
          57       15218
          58       15728
          59       16346
          60       16880
          61       17474
          62       17984
          63       18578
          64       19232
          65       19802
          66       20432
          67       21074
          68       21704
          69       22322
          70       23072
          71       23642
          72       24296
          73       24962
          74       25712
          75       26426
          76       27056
          77       27866
          78       28616
          79       29234
          80       30104
          81       30842
          82       31520
          83       32330
          84       33128
          85       33986
          86       34712
          87       35546
          88       36440
          89       37082
          90       38120
          91       38930
          92       39728
          93       40634
          94       41504
          95       42482
          96       43256
          97       44210
          98       45128
          99       46010
         100       47000