|
| |
|
|
A000980
|
|
Number of ways of writing 0 as Sum_{k=-n..n} e(k)*k, where e(k) is 0 or 1.
(Formerly M1155 N0439)
|
|
7
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
S. R. Finch, Signum equations and extremal coefficients.
|
|
|
FORMULA
| 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
a(n) = A004171(n) - 2*A181765(n).
Coefficient of x^(n*(n+1)/2) in 2*prod(k=1..n,(1+x^k)^2). [Sean A. Irvine, Oct 03 2011]
|
|
|
MATHEMATICA
| a[n_] := SeriesCoefficient[ Product[1+x^k, {k, -n, n}], {x, 0, 0}]; a[0] = 2; Table[a[n], {n, 0, 24}](* From Jean-François Alcover, Nov 28 2011 *)
|
|
|
PROG
| (PARI) a(n)=polcoeff(prod(k=-n, n, 1+x^k), 0)
(Haskell) a000980 n = length $ filter ((== 0) . sum) $ subsequences [-n..n]
|
|
|
CROSSREFS
| A047653(n)=a(n)/2.
Bisection of A084239. Cf. A063865, A141000.
Sequence in context: A115219 A078160 A089976 * A123611 A082279 A113180
Adjacent sequences: A000977 A000978 A000979 * A000981 A000982 A000983
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Michael Somos, Jun 10, 2000.
|
| |
|
|
