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Search: id:A025591
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| A025591 |
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Maximal coefficient of Product_{k<=n} (x^k+1). Number of solutions to +- 1 +- 2 +- 3 +- ... +- n = 0 or 1. |
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+0
19
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| 1, 1, 1, 2, 2, 3, 5, 8, 14, 23, 40, 70, 124, 221, 397, 722, 1314, 2410, 4441, 8220, 15272, 28460, 53222, 99820, 187692, 353743, 668273, 1265204, 2399784, 4559828, 8679280, 16547220, 31592878, 60400688, 115633260, 221653776, 425363952, 817175698
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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If k is allowed to approach infinity, this gives the partition numbers A000009.
a(n) is the maximal number of subsets of {1,2,...,n} that share the same sum.
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REFERENCES
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Robert A. Proctor, Solution of two difficult combinatorial problems with linear algebra, American Mathematical Monthly 89, 721-734.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
Dorin Andrica and Ioan Tomescu, On an Integer Sequence Related to a Product..., Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.4
E. Friedman and M. Keith, Magic Carpets, J. Int Sequences, 3 (2000), #P.00.2.5.
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MATHEMATICA
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f[n_, s_] := f[n, s]=Which[n==0, If[s==0, 1, 0], Abs[s]>(n*(n+1))/2, 0, True, f[n-1, s-n]+f[n-1, s+n]]; Table[Which[Mod[n, 4]==0||Mod[n, 4]==3, f[n, 0], Mod[n, 4]==1||Mod[n, 4]==2, f[n, 1]], {n, 0, 40}]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(prod(k=1, n, 1+x^k), n*(n+1)\4))
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CROSSREFS
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Cf. A063865, A063866, A063867, A083309, A083527.
Sequence in context: A018136 A022863 A039822 this_sequence A028409 A080553 A141602
Adjacent sequences: A025588 A025589 A025590 this_sequence A025592 A025593 A025594
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KEYWORD
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nonn,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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