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A135706
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a(n) = n*(5*n-3).
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12
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0, 2, 14, 36, 68, 110, 162, 224, 296, 378, 470, 572, 684, 806, 938, 1080, 1232, 1394, 1566, 1748, 1940, 2142, 2354, 2576, 2808, 3050, 3302, 3564, 3836, 4118, 4410, 4712, 5024, 5346, 5678, 6020, 6372, 6734, 7106, 7488, 7880, 8282, 8694, 9116, 9548, 9990, 10442
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Binomial transform of [2, 12, 10, 0, 0, 0, ...]. - Gary W. Adamson, Mar 05 2008
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 2*x*(1 + 4*x)/(1 - x)^3.
E.g.f.: x*(2 + 5*x)*exp(x). (End)
Sum_{n>=1} 1/a(n) = tan(Pi/10)*Pi/6 - sqrt(5)*log(phi)/6 + 5*log(5)/12, where phi is the golden ratio (A001622). - Amiram Eldar, Jul 19 2022
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {0, 2, 14}, 50] (* or *) Table[n*(5*n-3), {n, 0, 50}] (* G. C. Greubel, Oct 29 2016 *)
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PROG
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CROSSREFS
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Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488 (this sequence is the case k=10). - Bruno Berselli, Jun 10 2013
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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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