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A007576
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Number of solutions to k_1+2*k_2+..+n*k_n=0, where k_i are from {-1,0,1}, i=1..n.
(Formerly M2656)
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5
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1, 1, 1, 3, 7, 15, 35, 87, 217, 547, 1417, 3735, 9911, 26513, 71581, 194681, 532481, 1464029, 4045117, 11225159, 31268577, 87404465, 245101771, 689323849, 1943817227, 5494808425, 15568077235, 44200775239, 125739619467
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Also, number of maximally stable towers of 2 X 2 LEGO blocks.
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. J. S. Watson, On "LEGO" towers, J. Rec. Math., 12 (No. 1, 1979-1980), 24-27.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
S. R. Finch, Signum equations and extremal coefficients.
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FORMULA
| Coefficient of x^(n*(n+1)/2) in Product_{k=1..n} (1+x^k+x^(2*k)).
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EXAMPLE
| For n=4 there are 7 solutions: (-1,-1,1,0), (-1,0,-1,1), (-1,1,1,-1), (0,0,0,0), (1,-1,-1,1), (1,0,1,-1), (1,1,-1,0).
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MATHEMATICA
| f[0] = 1; f[n_] := Coefficient[Expand@ Product[1 + x^k + x^(2k), {k, n}], x^(n(n + 1)/2)]; Table[f@n, {n, 0, 28}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 10 2006)
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PROG
| (Maxima) a(n):=coeff(expand(product(1+x^k+x^(2*k), k, 1, n)), x, binomial(n+1, 2));
makelist(a(n), n, 0, 24);
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CROSSREFS
| Cf. A007575, A063865, A039826.
Sequence in context: A124696 A081669 A086821 * A167539 A183557 A190571
Adjacent sequences: A007573 A007574 A007575 * A007577 A007578 A007579
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KEYWORD
| easy,nonn
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AUTHOR
| Simon Plouffe, Robert G. Wilson v (rgwv(AT)rgwv.com) and Vladeta Jovovic (vladeta(AT)eunet.rs)
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 29 2005
Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 07 2006. This is a merging of two sequences which thanks to the work of Soren Eilers we now know are identical.
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