A151490 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), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 1)}.

1, 1, 5, 18, 88, 420, 2205, 11725, 64974, 365610, 2104536, 12269796, 72582840, 433722432, 2618401071, 15934054422, 97711687502, 603038843550, 3744098645430, 23367526504608, 146547154251576, 923028365663976, 5836943944538460, 37044904706130360, 235900143031713432, 1506833812242911480

Offset

0,3

Links

Table of n, a(n) for n=0..25.

M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, ArXiv 0810.4387, 2008.

Maple

ogf := Int(Int((2*(12*x^2+1)*hypergeom([1/4, 3/4], [1], 64*(x^2+x+1)*x^2/(12*x^2+1)^2)-2*x*(8*x+1)*hypergeom([3/4, 5/4], [2], 64*(x^2+x+1)*x^2/(12*x^2+1)^2))/((1-4*x-20*x^2)*(12*x^2+1)^(3/2)), x), x)/x^2;
series(ogf, x=0, 20); # Mark van Hoeij, Aug 20 2014

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[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, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A156305 A369362 A213190 * A282475 A185652 A009305

Adjacent sequences: A151487 A151488 A151489 * A151491 A151492 A151493

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved