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Search: id:A005559
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| A005559 |
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Number of walks on square lattice.
(Formerly M1832)
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+0
3
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| 1, 2, 8, 20, 75, 210, 784, 2352, 8820, 27720, 104544, 339768, 1288287, 4294290, 16359200, 55621280, 212751396, 734959368, 2821056160, 9873696560, 38013731756
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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) = C(n+2, ceil(n/2))*C(n+1, floor(n/2)) - C(n+2, ceil((n-1)/2))*C(n+1, floor((n-1)/2)). - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2004
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PROGRAM
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(PARI) {a(n)=binomial(n+2, ceil(n/2))*binomial(n+1, floor(n/2)) - binomial(n+2, ceil((n-1)/2))*binomial(n+1, floor((n-1)/2))}
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CROSSREFS
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Cf. A005558-A005560, A093768.
Sequence in context: A100097 A133467 A091004 this_sequence A001471 A162585 A000159
Adjacent sequences: A005556 A005557 A005558 this_sequence A005560 A005561 A005562
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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