A151474 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, -1), (-1, 0), (0, -1), (0, 1), (1, 0), (1, 1)}.

1, 1, 5, 16, 72, 310, 1458, 6954, 34290, 171942, 877782, 4539912, 23760136, 125569340, 669355076, 3594689358, 19432582910, 105666075398, 577578487822, 3171950427216, 17493908318976, 96855235817940, 538131805091196, 2999543610350100, 16769107205048772, 94005494978098780, 528319382998160540

Offset

0,3

Links

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

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

Crossrefs

Sequence in context: A332470 A151465 A363299 * A138550 A363558 A197052

Adjacent sequences: A151471 A151472 A151473 * A151475 A151476 A151477

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved