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A097063
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Expansion of (1-2x+3x^2)/((1+x)(1-x)^3).
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2
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1, 0, 3, 4, 9, 12, 19, 24, 33, 40, 51, 60, 73, 84, 99, 112, 129, 144, 163, 180, 201, 220, 243, 264, 289, 312, 339, 364, 393, 420, 451, 480, 513, 544, 579, 612, 649, 684, 723, 760, 801, 840, 883, 924, 969, 1012, 1059, 1104, 1153, 1200, 1251, 1300, 1353, 1404
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Partial sums of A097062. Pairwise sums are A002061. Binomial transform is essentially A007466.
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FORMULA
| G.f. : (1-2x+3x^2)/((1-x^2)(1-x)^2); a(n)=2a(n-1)-2a(n-3)+a(n-4); a(n)=sum{k=0..n, (k^2-k+1)(-1)^(n-k) }.
a(n)=1/4+(3/4)*(-1)^n+(1/2)*n^2, n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 10 2008
a(2n)=A058331(n). a(2n+1)=A046092(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 27 2008]
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CROSSREFS
| Sequence in context: A155564 A105137 A025613 * A026476 A002513 A034418
Adjacent sequences: A097060 A097061 A097062 * A097064 A097065 A097066
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 22 2004
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