A166873 a(n) = a(n-1) + 12*n for n > 1; a(1) = 1.
1, 25, 61, 109, 169, 241, 325, 421, 529, 649, 781, 925, 1081, 1249, 1429, 1621, 1825, 2041, 2269, 2509, 2761, 3025, 3301, 3589, 3889, 4201, 4525, 4861, 5209, 5569, 5941, 6325, 6721, 7129, 7549, 7981, 8425, 8881, 9349, 9829, 10321, 10825, 11341, 11869
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Programs
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Magma
[ n eq 1 select 1 else Self(n-1)+12*n: n in [1..44] ];
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Mathematica
LinearRecurrence[{3,-3,1},{1,25,61},50] (* G. C. Greubel, May 27 2016 *) -
PARI
a(n)=6*n^2+6*n-11 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = 6*n^2 + 6*n - 11.
a(n) = 2*a(n-1) - a(n-2) + 12.
G.f.: x*(1 + 22*x - 11*x^2)/(1-x)^3.
a(n) - a(n-1) = A008594(n) for n > 1.
From G. C. Greubel, May 27 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
E.g.f.: (-11 + 12*x + 6*x^2)*exp(x) + 11. (End)
Comments