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Search: id:A000128
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| A000128 |
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A nonlinear binomial sum.
(Formerly M1120 N0428)
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+0
1
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| 1, 2, 4, 8, 16, 31, 58, 105, 185, 319, 541, 906, 1503, 2476, 4058, 6626, 10790, 17537, 28464, 46155, 74791, 121137, 196139, 317508, 513901, 831686, 1345888, 2177900, 3524140, 5702419, 9226966, 14929821, 24157253, 39087571, 63245353, 102333486
(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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
D. A. Lind, On a class of nonlinear binomial sums, Fib. Quart., 3 (1965), 292-298.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..201
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.
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FORMULA
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G.f.: (1 - 2 x + x^2 + x^3 ) / ( 1 - x - x^2 ) ( 1 - x )^3.
Fib(n+4) - n(n+1)/2 - 3, with Fib(n) = A000045(n). - Ralf Stephan, Aug 19 2004
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MAPLE
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A000128:=(1-2*z+z**2+z**3)/(z**2+z-1)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Differences are A000126.
Sequence in context: A056183 A000127 A133552 this_sequence A106399 A007800 A102726
Adjacent sequences: A000125 A000126 A000127 this_sequence A000129 A000130 A000131
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Oct 06 2002
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