A080861 a(n) = 15*n^2 + 6*n + 1.

1, 22, 73, 154, 265, 406, 577, 778, 1009, 1270, 1561, 1882, 2233, 2614, 3025, 3466, 3937, 4438, 4969, 5530, 6121, 6742, 7393, 8074, 8785, 9526, 10297, 11098, 11929, 12790, 13681, 14602, 15553, 16534, 17545, 18586, 19657, 20758, 21889, 23050, 24241, 25462, 26713, 27994

Offset

0,2

Comments

The old definition of this sequence was "Generalized polygonal numbers".

Column T(n,6) of A080853.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = C(6,0) + C(6,1)*n + C(6,2)*n^2.

G.f.: (C(5,0) + (C(7,2)-2)*x + C(5,2)*x^2)/(1-x)^3 = (1 + 19*x + 10*x^2)/(1-x)^3.

From Elmo R. Oliveira, Oct 20 2024: (Start)

E.g.f.: exp(x)*(1 + 21*x + 15*x^2).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

Mathematica

CoefficientList[Series[(1 + 19 x + 10 x^2) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 05 2013 *)
LinearRecurrence[{3, -3, 1}, {1, 22, 73}, 40] (* Harvey P. Dale, Sep 28 2019 *)

Prog

(Magma) [15*n^2 + 6*n + 1 : n in [0..40]]; // Vincenzo Librandi, Aug 05 2013
(PARI) a(n)=15*n^2+6*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A080853.

Sequence in context: A044160 A044541 A251286 * A241521 A143838 A282723

Adjacent sequences: A080858 A080859 A080860 * A080862 A080863 A080864

Keyword

nonn,easy

Author

Paul Barry, Feb 23 2003

Extensions

Definition replaced with the closed form by Bruno Berselli, Jan 16 2013

Status

approved