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Search: id:A151162
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| A151162 |
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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)} |
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+0
8
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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Hankel transform is 3^C(n+1,2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 01 2009]
Inverse binomial transform of A151253 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 03 2009]
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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FORMULA
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a(n)=sum{k=0..n, A120730(n,k)*3^k}. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 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 DELEHAM (kolotoko(AT)wanadoo.fr), Feb 02 2009]
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MATHEMATICA
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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}]
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CROSSREFS
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Adjacent sequences: A151159 A151160 A151161 this_sequence A151163 A151164 A151165
Sequence in context: A085481 A030195 A114515 this_sequence A094547 A026559 A008781
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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