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Search: id:A135037
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| A135037 |
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Sums of the products of n consecutive triples of numbers. |
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+0
1
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| 0, 60, 396, 1386, 3570, 7650, 14490, 25116, 40716, 62640, 92400, 131670, 182286, 246246, 325710, 423000, 540600, 681156, 847476, 1042530, 1269450, 1531530, 1832226, 2175156, 2564100, 3003000, 3495960, 4047246, 4661286, 5342670
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(1) = 0*1*2 a(2) = 0*1*2 + 3*4*5 ..., a(n) = 0*1*2 + 3*4*5 + 6*7*8 + ... + (2n-1)*(2n)*(2n+1)
a(n) = (27n^4-18n^3-15n^2+6n)/4.
O.g.f.: -6*x^2*(10+16*x+x^2)/(-1+x)^5 . a(n) = 6*A024391(n-1) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 14 2008
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EXAMPLE
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For n = 3, the sum of the first 3 triples is 0*1*2+3*4*5+6*7*8 =396, the 3rd entry in the sequence.
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PROGRAM
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(PARI) sumprod3(n) = { local(x, s=0); forstep(x=0, n, 3, s+=x*(x+1)*(x+2); print1(s", ") ) }
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CROSSREFS
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Adjacent sequences: A135034 A135035 A135036 this_sequence A135038 A135039 A135040
Sequence in context: A056419 A060489 A088942 this_sequence A020868 A088943 A097387
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Feb 10 2008
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