A094060 Number of walks of length n on hexagonal grid that start and end at the origin. Intermediate returns to the origin are not permitted.

1, 0, 6, 12, 54, 216, 1032, 4896, 24606, 125040, 651348, 3432168, 18331992, 98814816, 537343632, 2942475552, 16214888286, 89835783264, 500116783740, 2795958732024, 15690597591636, 88354191756816, 499060719941616, 2826794871554112, 16052536475622792

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1291 (first 97 terms from Ludovic Schwob)

Formula

INVERTi transform of A002898. - R. J. Mathar, Sep 29 2020

Maple

b:= proc(n) option remember; `if`(n<3, [1, 0, 6][n+1], ((n-1)*
      n*b(n-1) +24*(n-1)^2*b(n-2) +36*(n-1)*(n-2)*b(n-3))/n^2)
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      b(n)-add(a(n-i)*b(i), i=1..n-1))
    end:
seq(a(n), n=0..23);  # Alois P. Heinz, Dec 07 2020

Mathematica

b[n_] := b[n] = If[n<3, {1, 0, 6}[[n+1]], ((n-1)n b[n-1] + 24(n-1)^2* b[n-2] + 36(n-1)(n-2) b[n-3])/n^2];
a[n_] := a[n] = If[n==0, 1, b[n] - Sum[a[n-i] b[i], {i, 1, n-1}]];
a /@ Range[0, 23] (* Jean-François Alcover, Jan 14 2021, after Alois P. Heinz *)

Crossrefs

Cf. A002898, A054474.

Sequence in context: A117866 A365691 A290999 * A341893 A324529 A076722

Adjacent sequences: A094057 A094058 A094059 * A094061 A094062 A094063

Keyword

nonn,walk

Author

Gareth McCaughan (gareth.mccaughan(AT)pobox.com), Jun 10 2004

Status

approved