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

1,2

Comments

Binomial transform of 1,24,12,0,0,0,....

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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)

Mathematica

LinearRecurrence[{3, -3, 1}, {1, 25, 61}, 50] (* G. C. Greubel, May 27 2016 *)

Prog

(Magma) [ n eq 1 select 1 else Self(n-1)+12*n: n in [1..44] ];
(PARI) a(n)=6*n^2+6*n-11 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A008594 (multiples of 12).

A000217, A028387, A133694, A059993, A166137, A166143, A166146, A166147, A166148, A166150, A166144 have recurrence a(n-1)+k*n with a(1)=1 or a(0)=1 for k = 1..11 resp.

Sequence in context: A090820 A044127 A044508 * A242317 A251688 A211326

Adjacent sequences: A166870 A166871 A166872 * A166874 A166875 A166876

Keyword

easy,nonn

Author

Klaus Brockhaus, Oct 22 2009

Status

approved