A350561 - OEIS

%I #30 Feb 22 2022 00:39:56

%S 1,4,12,60,400,2960,24600,221072,2076744,20123080,197757768,

%T 1937125160,18687793880,175793675328,1594744777464,13794351556920,

%U 112576101214496,857945953884624,6037935953538456,38729529837059648,222984258240522544,1133096911619304064,4985812137371331624

%N a(n) is the number of ways of making n moves in English Peg Solitaire.

%C This sequence has 32 terms in total.

%e Given the positions marked thus:

%e       a b c

%e       d e f

%e   g h i j k l m

%e   n o p q r s t

%e   u v w x y z 0

%e       1 2 3

%e       4 5 6

%e there are 12 ways to make two moves, viz.,

%e    (1) e jumps over j, then h jumps over i;

%e    (2) e jumps over j, then x jumps over q;

%e    (3) e jumps over j, then l jumps over k;

%e    (4) o jumps over p, then d jumps over i;

%e    (5) o jumps over p, then 1 jumps over w;

%e    (6) o jumps over p, then r jumps over q;

%e    (7) 2 jumps over x, then j jumps over q;

%e    (8) 2 jumps over x, then v jumps over w;

%e    (9) 2 jumps over x, then z jumps over y;

%e   (10) s jumps over r, then f jumps over k;

%e   (11) s jumps over r, then p jumps over q;

%e   (12) s jumps over r, then 3 jumps over y.

%Y Cf. A335656, A350998.

%K nonn,fini

%O 0,2

%A _Douglas Boffey_, Jan 28 2022