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A052177
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Number of walks on simple cubic lattice (starting on the xy plane, never going below it and finishing a height 1 above it).
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1
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0, 1, 8, 50, 288, 1605, 8824, 48286, 264128, 1447338, 7953040, 43842788, 242507456, 1345868589, 7493458392, 41850173670, 234408444288, 1316541032958, 7413214297968, 41842633282620, 236703844320960
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
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FORMULA
| a(n) = 4*a(n-1)+A005572(n-1)+A052178(n-1) = A052179(n, 1) = sum{j = 0, ..., ceiling[(n-1)/2]}[4^(n-2j-1)*C(n, 2j+1)*C(2j+2, j+1)/(j+2).
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CROSSREFS
| Sequence in context: A133357 A081675 A081180 * A115598 A127745 A037547
Adjacent sequences: A052174 A052175 A052176 * A052178 A052179 A052180
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 26 2000
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EXTENSIONS
| More terms and formula from Henry Bottomley (se16(AT)btinternet.com), Aug 23 2001
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