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A151387
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, 0), (1, -1), (1, 1)}.
0
1, 2, 10, 74, 636, 5996, 60500, 640536, 7032004, 79442404, 918460996, 10822792116, 129586488144, 1572865007248, 19316089471728, 239655258634016, 3000258698957516, 37860881282339972, 481184329951150276, 6154697345463251892, 79178658464829291656, 1023964603651763072264
OFFSET
0,2
LINKS
M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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, 1 + j, -1 + n] + aux[1 + i, 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: A228609 A001395 A047853 * A349310 A192259 A245901
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved