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A151254 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1)} 6
1, 4, 20, 96, 480, 2368, 11840, 58880, 294400, 1468416, 7342080, 36667392, 183336960, 916144128, 4580720640, 22896574464, 114482872320, 572320645120, 2861603225600, 14306741583872, 71533707919360, 357650927714304, 1788254638571520, 8941026626502656, 44705133132513280, 223522175800311808 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is 4^C(n+1,2). [From Philippe Deléham, Feb 01 2009]

LINKS

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

P. Barry, A Note on a One-Parameter Family of Catalan-Like Numbers, JIS 12 (2009) 09.5.4

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

FORMULA

a(n)=sum{k=0..n, A120730(n,k)*4^k}. [From Philippe Deléham, Feb 01 2009]

a(2n+2)=5*a(2n+1), a(2n+1)=5*a(2n)-4^n*A000108(n)=5*a(2n)-A151403(n). G.f.: (sqrt(1-16*x^2)+8x-1)/(8x*(1-5x)). [From Philippe Deléham, Feb 02 2009]

MATHEMATICA

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A250162 A296665 A057087 * A232493 A240778 A293710

Adjacent sequences:  A151251 A151252 A151253 * A151255 A151256 A151257

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 24 11:06 EST 2018. Contains 299603 sequences. (Running on oeis4.)