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A080861 15*n^2 + 6*n + 1. 2
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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

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Last modified August 4 13:19 EDT 2020. Contains 336201 sequences. (Running on oeis4.)