A151441 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, 1), (0, 1), (1, 0), (1, 1)}.

1, 1, 4, 12, 47, 176, 731, 2988, 12813, 55048, 241623, 1067940, 4776698, 21504298, 97577393, 445194901, 2042702372, 9415233073, 43584936370, 202517766967, 944273642108, 4416498692067, 20715830918990, 97422299663122, 459262944148012, 2169843807367587, 10272842737563387, 48728556603498579

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[1 + i, -1 + 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: A149375 A035310 A022016 * A361428 A032380 A057346

Adjacent sequences: A151438 A151439 A151440 * A151442 A151443 A151444

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved