

A151406


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), (0, 1), (1, 1), (1, 1)}


0



1, 0, 1, 2, 4, 8, 31, 74, 180, 598, 1834, 4788, 14996, 49482, 143789, 435354, 1453804, 4561596, 13938918, 45872900, 150436644, 473005586, 1538113866, 5131580610, 16631971200, 54060256628, 180817311524, 599398780812, 1965766211768, 6566285301920, 22047832597671, 73217323048944, 244741654013110
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OFFSET

0,4


LINKS

Table of n, a(n) for n=0..32.
M. BousquetMÃ©lou 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, 1 + j, 1 + n] + aux[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: A326330 A018355 A100083 * A307611 A053147 A128055
Adjacent sequences: A151403 A151404 A151405 * A151407 A151408 A151409


KEYWORD

nonn,walk


AUTHOR

Manuel Kauers, Nov 18 2008


STATUS

approved



