A151387 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (1, -1), (1, 1)}.

1, 2, 10, 74, 636, 5996, 60500, 640536, 7032004, 79442404, 918460996, 10822792116, 129586488144, 1572865007248, 19316089471728, 239655258634016, 3000258698957516, 37860881282339972, 481184329951150276, 6154697345463251892, 79178658464829291656, 1023964603651763072264

Offset

0,2

Links

Table of n, a(n) for n=0..21.

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, 1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]

Crossrefs

Sequence in context: A228609 A001395 A047853 * A349310 A192259 A245901

Adjacent sequences: A151384 A151385 A151386 * A151388 A151389 A151390

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved