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A117066
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Partial sums of cupolar numbers (1/3)*(n+1)*(5*n^2+7*n+3) A096000.
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1
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1, 11, 48, 140, 325, 651, 1176, 1968, 3105, 4675, 6776, 9516, 13013, 17395, 22800, 29376, 37281, 46683, 57760, 70700, 85701, 102971, 122728, 145200, 170625, 199251, 231336, 267148, 306965, 351075, 98400, 105903, 399776, 453376, 512193, 576555, 646800, 723276, 806341
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n) = SUM[i=1..n] A096000(i). a(n) = SUM[i=1..n] (1/3)*(i+1)*(5*i^2+7*i+3). a(n) = SUM[i=1..n] (1/2)*(Q(i) + 3*i^2 + 3*i + 1), where Q(i) are the cuboctahedral numbers, A005902.
a(n) = sum{k=0..n} A073254(n,k)*k. - Peter Luschny, Oct 29 2011
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MAPLE
| a:=n->sum ((n+j)^3, j=0..n): seq(a(n)/9, n=1..37); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 17 2008]
with(finance):seq(add(cashflows([n^3, k^3, 0], 0 )/3, k=0..n), n=1..45); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
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MATHEMATICA
| Table[Sum[i*(n+i)*n, {i, 0, n}]/2, {n, 1, 100}] (* From Vladimir Joseph Stephan Orlovsky, June 03 2011 *)
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CROSSREFS
| Cf. A005902, A096000.
Sequence in context: A191499 A072372 A024530 * A042984 A008780 A101992
Adjacent sequences: A117063 A117064 A117065 * A117067 A117068 A117069
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 17 2006
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