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Search: id:A064045
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| A064045 |
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Square array read by antidiagonals of number of length 2k walks on an n-dimensional hypercubic lattice starting and finishing at the origin and staying in the nonnegative part. |
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+0
3
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| 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 10, 3, 1, 0, 14, 70, 24, 4, 1, 0, 42, 588, 285, 44, 5, 1, 0, 132, 5544, 4242, 740, 70, 6, 1, 0, 429, 56628, 73206, 16016, 1525, 102, 7, 1, 0, 1430, 613470, 1403028, 410928, 43470, 2730, 140, 8, 1, 0, 4862, 6952660, 29082339
(list; table; graph; listen)
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OFFSET
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0,8
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LINKS
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R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
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FORMULA
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a(n, k) = sum{j = 0, ..., k}[C(2k, 2j)c(j)a(n-1, k-j)] where c(j) = C(2j, j)/(j+1) = A000108(j) with a(0, 0) = 1
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EXAMPLE
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Rows start: {1, 0, 0, 0, 0, 0, 0,...}, {1, 1, 2, 5, 14, 42, 132,...}, {1, 2, 10, 70, 588, 5544, 56628,...}, {1, 3, 24, 285, 4242, 73206, 1403028,...},...
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CROSSREFS
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Rows include A000007, A000108, A005568, A064037. Columns include A000012, A001477, A049450, A064046. Cf. A064044.
Sequence in context: A067347 A120568 A065066 this_sequence A110314 A152882 A130167
Adjacent sequences: A064042 A064043 A064044 this_sequence A064046 A064047 A064048
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Aug 23 2001
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