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A013656
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a(n) = n*(9*n-2).
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4
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0, 7, 32, 75, 136, 215, 312, 427, 560, 711, 880, 1067, 1272, 1495, 1736, 1995, 2272, 2567, 2880, 3211, 3560, 3927, 4312, 4715, 5136, 5575, 6032, 6507, 7000, 7511, 8040, 8587, 9152, 9735, 10336, 10955, 11592, 12247, 12920, 13611, 14320, 15047, 15792, 16555
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OFFSET
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0,2
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COMMENTS
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For n>0, numbers such that sqrt(a(n)) has the continued fraction {k;[1,1,1,2k]}, where the part in [] is repeated and k is of the form 3m+2 (A016789). - Bruno Berselli, May 30 2013
For n >= 1, the continued fraction expansion of sqrt(4*a(n)) is [6n-1; {3, 3n-1, 3, 12n-2}]. - Magus K. Chu, Sep 18 2022
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LINKS
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FORMULA
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a(0)=0, a(1)=7, a(2)=32, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jul 07 2012
G.f.: x*(7 - 11*x)/(1-x)^3.
E.g.f.: x*(7 + 9*x)*exp(x). (End)
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MATHEMATICA
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Table[n(9n-2), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 7, 32}, 50] (* Harvey P. Dale, Jul 07 2012 *)
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PROG
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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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