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A264445
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a(n) = n*(n + 11)*(n + 22)/6.
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7
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0, 46, 104, 175, 260, 360, 476, 609, 760, 930, 1120, 1331, 1564, 1820, 2100, 2405, 2736, 3094, 3480, 3895, 4340, 4816, 5324, 5865, 6440, 7050, 7696, 8379, 9100, 9860, 10660, 11501, 12384, 13310, 14280, 15295, 16356, 17464, 18620, 19825, 21080
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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 = 11.
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LINKS
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FORMULA
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O.g.f.: x*(35*x^2 - 80*x + 46)/(1 - x)^4.
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MAPLE
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seq( n*(n + 11)*(n + 22)/6, n = 0..40 );
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {0, 46, 104, 175}, 50] (* Harvey P. Dale, Dec 11 2018 *)
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PROG
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(PARI) vector(100, n, n--; n*(n+11)*(n+22)/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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