A151433 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, 0), (1, 1)}.

1, 3, 23, 242, 2987, 40663, 591642, 9033815, 143086147, 2332577417, 38920508426, 661997451570, 11442777854792, 200524118645298, 3555829498671923, 63707928582145553, 1151818635756842038, 20992564017982373175, 385356783440628359148, 7119667287556648713060, 132307647760313085491973

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

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

Maple

b:= proc(n, l) b(n, l):= `if`(l[1]<0 or l[2]<0 or n<l[1], 0, `if`(n=0, 1,
       add(b(n-1, l+d), d=[[-1, -1], [-1, 0], [1, -1], [1, 0], [1, 1]])))
    end:
a:= n-> b(2*n, [0$2]):
seq (a(n), n=0..30);  # Alois P. Heinz, Jul 19 2012

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[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: A278745 A122009 A360987 * A199750 A318004 A098681

Adjacent sequences: A151430 A151431 A151432 * A151434 A151435 A151436

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved