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A151090 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, -1, -1), (-1, -1, 0), (0, 0, 1), (0, 1, 0), (1, 1, 1)} 1
1, 3, 11, 43, 175, 731, 3111, 13427, 58591, 257947, 1143943, 5104419, 22896303, 103169899, 466725143, 2118787187, 9648585791, 44060516667, 201709358631, 925531659971, 4255568177615, 19604179972363, 90468636882231, 418164385032723, 1935725673812575, 8973094439246811, 41648668456569671 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Xiang-Ke Chang, XB Hu, H Lei, YN Yeh, Combinatorial proofs of addition formulas, The Electronic Journal of Combinatorics, 23(1) (2016), #P1.8.

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.

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A026671 A026876 A270447 * A059278 A151091 A151092

Adjacent sequences:  A151087 A151088 A151089 * A151091 A151092 A151093

KEYWORD

nonn,walk,changed

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified December 5 16:08 EST 2016. Contains 278770 sequences.