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A350561 a(n) is the number of ways of making n moves in English Peg Solitaire.

%I A350561 #30 Feb 22 2022 00:39:56
%S A350561 1,4,12,60,400,2960,24600,221072,2076744,20123080,197757768,
%T A350561 1937125160,18687793880,175793675328,1594744777464,13794351556920,
%U A350561 112576101214496,857945953884624,6037935953538456,38729529837059648,222984258240522544,1133096911619304064,4985812137371331624
%N A350561 a(n) is the number of ways of making n moves in English Peg Solitaire.
%C A350561 This sequence has 32 terms in total.
%e A350561 Given the positions marked thus:
%e A350561       a b c
%e A350561       d e f
%e A350561   g h i j k l m
%e A350561   n o p q r s t
%e A350561   u v w x y z 0
%e A350561       1 2 3
%e A350561       4 5 6
%e A350561 there are 12 ways to make two moves, viz.,
%e A350561    (1) e jumps over j, then h jumps over i;
%e A350561    (2) e jumps over j, then x jumps over q;
%e A350561    (3) e jumps over j, then l jumps over k;
%e A350561    (4) o jumps over p, then d jumps over i;
%e A350561    (5) o jumps over p, then 1 jumps over w;
%e A350561    (6) o jumps over p, then r jumps over q;
%e A350561    (7) 2 jumps over x, then j jumps over q;
%e A350561    (8) 2 jumps over x, then v jumps over w;
%e A350561    (9) 2 jumps over x, then z jumps over y;
%e A350561   (10) s jumps over r, then f jumps over k;
%e A350561   (11) s jumps over r, then p jumps over q;
%e A350561   (12) s jumps over r, then 3 jumps over y.
%Y A350561 Cf. A335656, A350998.
%K A350561 nonn,fini
%O A350561 0,2
%A A350561 _Douglas Boffey_, Jan 28 2022