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Search: id:A004320
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| 0, 3, 16, 50, 120, 245, 448, 756, 1200, 1815, 2640, 3718, 5096, 6825, 8960, 11560, 14688, 18411, 22800, 27930, 33880, 40733, 48576, 57500, 67600, 78975, 91728, 105966, 121800, 139345, 158720, 180048, 203456, 229075, 257040, 287490, 320568
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Consider the set B(n) = {1,2,3,...n}. Let a(0) = 0. Then a(n) = Sum [ b(i)^2 - b(j)^2] for all i, j = 1 to n, b(i) belongs to B(n). E.g. a(3) = (3^2-1^2) + (3^2-2^2) +(2^2-1^2)= 16. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 01 2001
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FORMULA
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G.f.: x(3+x)/(1-x)^5 - Paul Barry (pbarry(AT)wit.ie), Feb 27 2003
(n+2)*C(n+2,3) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2006
a(n)=A047929(n)/6 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
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MAPLE
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[seq ((n+2)*(binomial(n+2, 3)), n=0..45)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2006
a:=n->sum(sum((n^2-n)/6, j=0..n), k=0..n): seq(a(n), n=1..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
a:=n->sum(sum(binomial(n+1, n)*k/3, j=2..n), k=0..n): seq(a(n), n=1..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007
a:=n->(sum((numbperm(n, 3)), j=1..n)):seq(a(n)/6, n=2..38); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
a:=n->add(binomial(n, 2)+add(binomial(n, 2), j=1..n), j=0..n):seq(a(n)/3, n=1..35); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]
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MATHEMATICA
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f[n_]:=(n+(n+1)+(n+2))*(n-1)*n*(n+1)/18; 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: A147874 A092466 A152618 this_sequence A089363 A000574 A041233
Adjacent sequences: A004317 A004318 A004319 this_sequence A004321 A004322 A004323
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2006
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