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URL: https://oeis.org/A131464

⇱ A131464 - OEIS

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A131464
a(n) = 4*n^3 - 3*n^2 + 2*n - 1.
2
2, 23, 86, 215, 434, 767, 1238, 1871, 2690, 3719, 4982, 6503, 8306, 10415, 12854, 15647, 18818, 22391, 26390, 30839, 35762, 41183, 47126, 53615, 60674, 68327, 76598, 85511, 95090, 105359, 116342, 128063, 140546, 153815, 167894, 182807, 198578, 215231, 232790
OFFSET
1,1
FORMULA
From Vincenzo Librandi, Feb 12 2013: (Start)
G.f.: x*(2 + 15*x + 6*x^2 + x^3)/(1 - x)^4.
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). (End)
E.g.f.: 1 - exp(x)*(1 - 3*x - 9*x^2 - 4*x^3). - Stefano Spezia, Dec 06 2024
MATHEMATICA
CoefficientList[Series[(2 + 15 x + 6 x^2 + x^3)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2013 *)
Table[4n^3-3n^2+2n-1, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 23, 86, 215}, 40] (* Harvey P. Dale, May 05 2018 *)
PROG
(Magma) [4*n^3-3*n^2+2*n-1: n in [1..40]]; // Vincenzo Librandi, Feb 12 2013
(Magma) I:=[2, 23, 86, 215]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Feb 12 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jul 26 2007
STATUS
approved