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A135036
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Sums of the products of n consecutive pairs of numbers.
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0
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of integer solutions to 1-n <= x <= y <= z <= n-1 where x - 2*y + z is nonzero. - Michael Somos, Dec 27 2011
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FORMULA
| 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
| For n = 3, the sum of the first 3 pairs is 0*1+2*3+4*5 = 26, the 3rd entry in the sequence.
G.f. = 6*x^2 + 26*x^3 + 68*x^4 + 140*x^5 + 250*x^6 + 406*x^7 + 616*x^8 + 888*x^9 + ...
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PROG
| (PARI) sumprod(n) = { local(x, s=0); forstep(x=0, n, 2, s+=x*(x+1); print1(s", ") ) }
(PARI) {a(n) = n * (n - 1) * (4*n + 1) / 3} /* Michael Somos, Dec 27 2011 */
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CROSSREFS
| Sequence in context: A166728 A136892 A190095 * A166796 A001701 A175898
Adjacent sequences: A135033 A135034 A135035 * A135037 A135038 A135039
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Feb 10 2008
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