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Search: id:A005557
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| A005557 |
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Number of walks on square lattice.
(Formerly M5277)
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+0
5
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| 42, 132, 297, 572, 1001, 1638, 2548, 3808, 5508, 7752, 10659, 14364, 19019, 24794, 31878, 40480, 50830, 63180, 77805, 95004, 115101, 138446, 165416, 196416, 231880, 272272, 318087, 369852, 428127, 493506, 566618, 648128, 738738, 839188, 950257, 1072764
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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)= A009766(n+5, 5) =(n+1)*binomial(n+10, 4)/5.
G.f.: (42-120*x+135*x^2-70*x^3+14*x^4)/(1-x)^6; numerator polynomial is N(2;4, x) from A062991.
binomial(n,5)-binomial(n,3),n>=9. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 19 2006
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MAPLE
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[seq(binomial(n, 5)-binomial(n, 3), n=9..55)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 19 2006
A005557:=(42-120*z+135*z**2-70*z**3+14*z**4)/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sixth diagonal of Catalan triangle A033184. Sixth column of Catalan triangle A009766.
Sequence in context: A113518 A044293 A044674 this_sequence A045088 A002759 A044374
Adjacent sequences: A005554 A005555 A005556 this_sequence A005558 A005559 A005560
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms and formula from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 04 2001
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