A151400 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 0), (-1, 1), (0, -1), (1, 1)}.

1, 0, 2, 4, 10, 32, 108, 312, 1036, 3552, 11680, 39214, 136772, 471748, 1626866, 5722264, 20199400, 71116826, 252507746, 902188304, 3222655648, 11548005134, 41588468526, 150008189222, 541865647164, 1963642984244, 7131101379546, 25927597277242, 94455538469920, 344779963787714, 1260046402628588

Offset

0,3

Links

Table of n, a(n) for n=0..30.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

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[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A070900 A296003 A263662 * A363138 A367113 A365516

Adjacent sequences: A151397 A151398 A151399 * A151401 A151402 A151403

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved