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A151162 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)} 7
1, 3, 12, 45, 180, 702, 2808, 11097, 44388, 176418, 705672, 2812482, 11249928, 44903484, 179613936, 717517521, 2870070084, 11470898106, 45883592424, 183438670950, 733754683800, 2934026948196, 11736107792784, 46934017407594, 187736069630376, 750833732416212, 3003334929664848 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is 3^C(n+1,2). [From Philippe Deléham, Feb 01 2009]

Inverse binomial transform of A151253 . [From Philippe Deléham, Feb 03 2009]

LINKS

Table of n, a(n) for n=0..26.

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)*3^k}. [From Philippe Deléham, Feb 01 2009]

a(2n+2)=4*a(2n+1), a(2n+1)=4*a(2n)-3^n*A000108(n)=4*a(2n)-A005159(n). G.f.:(sqrt(1-12*x^2)+6x-1)/(6x*(1-4x)). [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, 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: A030195 A114515 A192467 * A094547 A026559 A188949

Adjacent sequences:  A151159 A151160 A151161 * A151163 A151164 A151165

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified August 27 21:58 EDT 2015. Contains 261098 sequences.