A151487 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), (1, 1)}.

1, 1, 5, 15, 73, 295, 1453, 6709, 33727, 166433, 854781, 4380061, 22915615, 120259717, 638778193, 3408006119, 18324864455, 98963982349, 537422614247, 2929848766089, 16039760431783, 88106400546275, 485589372122359, 2683957205776315, 14875692005980127, 82650245915910297, 460275298623542575

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[-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: A105451 A149651 A149652 * A101553 A149653 A149654

Adjacent sequences: A151484 A151485 A151486 * A151488 A151489 A151490

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved