A151370 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 1)}.

1, 0, 2, 3, 20, 60, 345, 1400, 7770, 36876, 204876, 1062600, 5984352, 32772168, 187727826, 1065491427, 6206538910, 36123454224, 213645926208, 1266954939822, 7593846587496, 45694598654640, 277066122022872, 1686973019649060, 10331412410444280, 63524084460496480, 392411097399517800

Offset

0,3

Links

Table of n, a(n) for n=0..26.

M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.

Formula

G.f.: Int(Int(2*hypergeom([3/4, 5/4],[2],64*(x^2+x+1)*x^2/(12*x^2+1)^2)/(12*x^2+1)^(3/2),x),x)/x^2. - Mark van Hoeij, Aug 17 2014

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]

Crossrefs

Sequence in context: A233410 A318765 A055814 * A041567 A338084 A087301

Adjacent sequences: A151367 A151368 A151369 * A151371 A151372 A151373

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved