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A264444
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a(n) = n*(n + 7)*(n + 14)/6.
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7
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0, 20, 48, 85, 132, 190, 260, 343, 440, 552, 680, 825, 988, 1170, 1372, 1595, 1840, 2108, 2400, 2717, 3060, 3430, 3828, 4255, 4712, 5200, 5720, 6273, 6860, 7482, 8140, 8835, 9568, 10340, 11152, 12005, 12900, 13838, 14820, 15847, 16920
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OFFSET
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0,2
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COMMENTS
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It is well-known, and easy to prove, that the product of 3 consecutive integers n*(n + 1)*(n + 2) is divisible by 6. It can be shown that the product of 3 integers in arithmetic progression n*(n + r)*(n + 2*r) is divisible by 6 if and only if r is not divisible by 2 or 3 (see A007310 for these numbers). This is the case r = 7.
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LINKS
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FORMULA
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O.g.f.: x*(13*x^2 - 32*x + 20)/(1 - x)^4.
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MAPLE
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seq( n*(n + 7)*(n + 14)/6, n = 0..40 );
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MATHEMATICA
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PROG
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(PARI) vector(100, n, n--; n*(n+7)*(n+14)/6) \\ Altug Alkan, Nov 15 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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