God's Algorithm out to 14q*

I've computed the count of positions out to 14 quarter turns.

First, positions at exactly the given distance:

 d  mod M + inv         mod M      positions
-- ------------ ------------- --------------
 0            1             1              1
 1            1             1             12
 2            5             5            114
 3           17            25           1068
 4          130           219          10011
 5         1031          1978          93840
 6         9393         18395         878880
 7        86183        171529        8221632
 8       802788       1601725       76843595
 9      7482382      14956266      717789576
10     69833772     139629194     6701836858
11    651613601    1303138445    62549615248
12   6079089087   12157779067   583570100997
13  56691773613  113382522382  5442351625028
14 528436196526 1056867697737 50729620202582
Next, positions at the given distance or less:
 d  mod M + inv         mod M      positions
-- ------------ ------------- --------------
 0            1             1              1
 1            2             2             13
 2            7             7            127
 3           24            32           1195
 4          154           251          11206
 5         1185          2229         105046
 6        10578         20624         983926
 7        96761        192153        9205558
 8       899549       1793878       86049153
 9      8381931      16750144      803838729
10     78215703     156379338     7505675587
11    729829304    1459517783    70055290835
12   6808918391   13617296850   653625391832
13  63500692004  126999819232  6095977016860
14 591936888530 1183867516969 56825597219442