A144391 a(n) = 3*n^2 + n - 1.

3, 13, 29, 51, 79, 113, 153, 199, 251, 309, 373, 443, 519, 601, 689, 783, 883, 989, 1101, 1219, 1343, 1473, 1609, 1751, 1899, 2053, 2213, 2379, 2551, 2729, 2913, 3103, 3299, 3501, 3709, 3923, 4143, 4369, 4601, 4839, 5083, 5333, 5589, 5851, 6119, 6393, 6673

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Leo Tavares, Illustration: Cropped Hexagons

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

Formula

a(n) = A135370(2*n).

First differences: a(n+1) - a(n) = A016957(n).

a(n) - A144390(n) = 6*n + 4 = A005843(n).

From R. J. Mathar, Oct 24 2008: (Start)

G.f.: x*(3 + 4*x - x^2)/(1 - x)^3.

a(n) = A049451(n) - 1. (End)

E.g.f.: (3*x^2 + 4*x - 1)*exp(x) + 1. - G. C. Greubel, Jul 19 2017

a(n) = 1 + Sum_{i = n-1..2*n-1} 2*i. - Bruno Berselli, Feb 16 2018

a(n) = A003215(n) - (n+1)*2. - Leo Tavares, Jul 04 2021

Mathematica

Table[3 n^2 + n - 1, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {3, 13, 29}, 50] (* Harvey P. Dale, Sep 18 2016 *)

Prog

(Magma) [3*n^2+n-1: n in [1..50]]; // Vincenzo Librandi, May 06 2011
(PARI) a(n)=3*n^2+n-1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A135370, A144390.

Sequence in context: A042269 A049043 A031378 * A024836 A227541 A023553

Adjacent sequences: A144388 A144389 A144390 * A144392 A144393 A144394

Keyword

nonn,easy

Author

Paul Curtz, Oct 02 2008

Extensions

Edited by R. J. Mathar, Oct 24 2008

More terms from Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Status

approved