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Search: id:A077414
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| 0, 4, 15, 36, 70, 120, 189, 280, 396, 540, 715, 924, 1170, 1456, 1785, 2160, 2584, 3060, 3591, 4180, 4830, 5544, 6325, 7176, 8100, 9100, 10179, 11340, 12586, 13920, 15345, 16864, 18480, 20196, 22015, 23940, 25974, 28120, 30381, 32760, 35260
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of independent components of a certain 3-tensor in n-space.
a(n) is the number of independent components of a 3-tensor t(a,b,c) which satisfies t(a,b,c)=t(b,a,c) and sum(t(a,a,c),a=1..n)=0 for all c, with a,b,c range 1..n. (3-tensor in n-dimensional space which is symmetric and traceless in one pair of its indices.)
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FORMULA
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a(n) = n*(binomial(n+1, 2)-1).
G.f.: (x^2)*(4-x)/(1-x)^4.
sum (n*j,j=2..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 12 2006
a(n)=sum(sum(j, j=2..n),k=1..n), n>=1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007
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MAPLE
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a:=n->sum(sum(j, j=2..n), k=1..n): seq(a(n), n=1..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007
a:=n->sum(sum(binomial(n+1, n)-binomial(j+1, j), j=2..n), k=0..n): seq(a(n), n=2..42); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007
with(finance):seq(add(cashflows([n*k, n, k], 0 ), k=0..n), n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
a:=n->(sum((numbcomp(n, 3)), j=0..n)):seq(a(n), n=2..37); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
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MATHEMATICA
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f[n_]:=n*(n-1)*(n+2)/2; s=0; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 08 2009]
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CROSSREFS
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Sequence in context: A124150 A054556 A113693 this_sequence A015653 A106199 A113289
Adjacent sequences: A077411 A077412 A077413 this_sequence A077415 A077416 A077417
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002
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EXTENSIONS
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More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 30 2006
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