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A007576 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)
6
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; text; internal format)
OFFSET

0,4

COMMENTS

Also, number of maximally stable towers of 2 X 2 LEGO blocks.

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.

LINKS

T. D. Noe and Ray Chandler, Table of n, a(n) for n = 0..2106 (terms < 10^1000, first 101 terms from T. D. Noe)

S. R. Finch, Signum equations and extremal coefficients.

P. J. S. Watson, On "LEGO" towers, J. Rec. Math., 12 (No. 1, 1979-1980), 24-27. (Annotated scanned copy)

Index entry for sequences related to LEGO blocks

FORMULA

Coefficient of x^(n*(n+1)/2) in Product_{k=1..n} (1+x^k+x^(2*k)).

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).

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}] (* Robert G. Wilson v, Nov 10 2006 *)

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);

CROSSREFS

Cf. A007575, A063865, A039826.

Sequence in context: A124696 A081669 A086821 * A167539 A223167 A183557

Adjacent sequences:  A007573 A007574 A007575 * A007577 A007578 A007579

KEYWORD

easy,nonn

AUTHOR

Simon Plouffe, Robert G. Wilson v and Vladeta Jovovic

EXTENSIONS

More terms from David Wasserman, Mar 29 2005

Edited by N. J. A. Sloane, Nov 07 2006. This is a merging of two sequences which, thanks to the work of Søren Eilers, we now know are identical.

STATUS

approved

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Last modified February 25 06:31 EST 2018. Contains 299643 sequences. (Running on oeis4.)