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A144314
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a(n) = 3*n*(6*n+1).
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6
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0, 21, 78, 171, 300, 465, 666, 903, 1176, 1485, 1830, 2211, 2628, 3081, 3570, 4095, 4656, 5253, 5886, 6555, 7260, 8001, 8778, 9591, 10440, 11325, 12246, 13203, 14196, 15225, 16290, 17391, 18528, 19701, 20910, 22155, 23436, 24753, 26106, 27495
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OFFSET
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0,2
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
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FORMULA
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a(n) = A000217(6*n) = A014105(3*n) = A081266(2*n).
a(n) = a(n-1)+36*n-15 for n>0, a(0)=0. - Vincenzo Librandi, Dec 27 2010
G.f.: x*(21+15*x)/(1-x)^3. - Vincenzo Librandi, Dec 18 2014
From Wesley Ivan Hurt, Dec 16 2015: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
a(n) = 3 * A049453(n). (End)
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MAPLE
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A144314:=n->3*n*(6*n+1): seq(A144314(n), n=0..70); # Wesley Ivan Hurt, Dec 16 2015
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MATHEMATICA
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Table[3n(6n+1), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 21, 78}, 40] (* Harvey P. Dale, Dec 17 2014 *)
CoefficientList[Series[x (21 + 15 x) / (1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 18 2014 *)
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PROG
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(MAGMA) [18*n^2+3*n: n in [0..50]]; // Vincenzo Librandi, Dec 18 2014
(PARI) a(n)=3*n*(6*n+1) \\ Charles R Greathouse IV, Oct 07 2015
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CROSSREFS
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Cf. A000217, A014105, A033585, A049453, A081266, A144312.
Sequence in context: A143206 A182754 A045559 * A010009 A172082 A296970
Adjacent sequences: A144311 A144312 A144313 * A144315 A144316 A144317
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KEYWORD
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nonn,easy
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AUTHOR
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Reinhard Zumkeller, Sep 17 2008
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STATUS
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approved
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