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Search: id:A000980
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| A000980 |
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Number of ways of writing 0 as Sum_{k=-n..n} e(k)*k, where e(k) is 0 or 1.
(Formerly M1155 N0439)
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+0
5
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| 2, 4, 8, 20, 52, 152, 472, 1520, 5044, 17112, 59008, 206260, 729096, 2601640, 9358944, 33904324, 123580884, 452902072, 1667837680, 6168510256, 22903260088, 85338450344, 318995297200, 1195901750512, 4495448217544
(list; graph; listen)
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OFFSET
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0,1
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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. 294.
R. C. Entringer, Representation of m as Sum_{k=-n..n} epsilon_k k, Canad. Math. Bull., 11 (1968), 289-293.
J. H. van Lint, Representations of 0 as Sum_{k = -N..N} epsilon_k*k, Proc. Amer. Math. Soc., 18 (1967), 182-184.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
S. R. Finch, Signum equations and extremal coefficients.
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FORMULA
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Constant term of prod(k=-n, n, 1+x^k).
a(n) = sum_i A067059(2n+1-i, i) = 2+2*sum_j A047997(n, j); i.e. sum of alternate antidiagonals of A067059 and two more than twice row sums of A047997. - Henry Bottomley (se16(AT)btinternet.com), Aug 11 2002
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PROGRAM
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(PARI) a(n)=polcoeff(prod(k=-n, n, 1+x^k), 0)
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CROSSREFS
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A047653(n)=a(n)/2.
Bisection of A084239. Cf. A063865, A141000.
Sequence in context: A115219 A078160 A089976 this_sequence A123611 A082279 A113180
Adjacent sequences: A000977 A000978 A000979 this_sequence A000981 A000982 A000983
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KEYWORD
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nonn,nice
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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 Michael Somos, Jun 10, 2000.
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