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Search: id:A135036
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| A135036 |
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Sums of the products of n consecutive pairs of numbers. |
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+0
1
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| 0, 6, 26, 68, 140, 250, 406, 616, 888, 1230, 1650, 2156, 2756, 3458, 4270, 5200, 6256, 7446, 8778, 10260, 11900, 13706, 15686, 17848, 20200, 22750, 25506, 28476, 31668, 35090, 38750, 42656, 46816, 51238, 55930, 60900, 66156, 71706, 77558, 83720
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = 1*2 + 3*4 + 5*6 + ... + 2n*(2n+1)
a(n) = (4n^3-3n^2-n)/3. For n=3, this gives (4*27-3*9-3)/3 = 78/3 = 26.
O.g.f.: 2*x^2*(3+x)/(-1+x)^4 . a(n) = 2*A016061(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 pairs is 0*1+2*3+4*5 = 26, the 3rd entry in the sequence.
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PROGRAM
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(PARI) sumprod(n) = { local(x, s=0); forstep(x=0, n, 2, s+=x*(x+1); print1(s", ") ) }
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CROSSREFS
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Adjacent sequences: A135033 A135034 A135035 this_sequence A135037 A135038 A135039
Sequence in context: A075454 A075456 A136892 this_sequence A001701 A094162 A060101
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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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