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A151393 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, 1), (1, 0), (1, 1)}. 1
1, 3, 23, 229, 2564, 30874, 390124, 5100052, 68384716, 935121688, 12988742454, 182726814050, 2597994569974, 37269939754622, 538769767630088, 7840164781172800, 114752711724862584, 1688183258963366500, 24948722231136735010, 370204576610120406342, 5513458878514541095188 (list; graph; refs; listen; history; text; internal format)
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) option remember; `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, 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, 1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]

CROSSREFS

Sequence in context: A201205 A068954 A068955 * A007781 A068146 A162591

Adjacent sequences:  A151390 A151391 A151392 * A151394 A151395 A151396

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified June 15 07:12 EDT 2021. Contains 345043 sequences. (Running on oeis4.)