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Search: id:A000115
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| A000115 |
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Denumerants: expansion of 1 /((1 - x)(1 - x^2)(1 - x^5)).
(Formerly M0279 N0098)
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+0
3
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| 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 16, 18, 20, 22, 24, 26, 29, 31, 34, 36, 39, 42, 45, 48, 51, 54, 58, 61, 65, 68, 72, 76, 80, 84, 88, 92, 97, 101, 106, 110, 115, 120, 125, 130, 135, 140, 146, 151, 157, 162, 168, 174, 180, 186, 192, 198, 205, 211, 218, 224, 231, 238
(list; graph; listen)
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OFFSET
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0,3
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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).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 120, D(n;1,2,5).
M. Jeger, Ein partitions problem ..., Elemente de Math., 13 (1958), 97-120.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 152.
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FORMULA
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round((n+4)^2/20).
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MAPLE
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1/((1-x)*(1-x^2)*(1-x^5));
(From Jeger's paper:) s:=proc(n) if n mod 5 = 0 then RETURN(1); fi; if n mod 5 = 1 then RETURN(0); fi; if n mod 5 = 2 then RETURN(1); fi; if n mod 5 = 3 then RETURN(-1); fi; if n mod 5 = 4 then RETURN(-1); fi; end; f:=n->(2*n^2+16*n+27+5*(-1)^n+8*s(n))/40;
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CROSSREFS
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First differences are in A008616. First differences of A001304. Pairwise sums of A008720.
Adjacent sequences: A000112 A000113 A000114 this_sequence A000116 A000117 A000118
Sequence in context: A118868 A017885 A011874 this_sequence A033552 A062420 A089197
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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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