A144390 a(n) = 3*n^2 - n - 1.

1, 9, 23, 43, 69, 101, 139, 183, 233, 289, 351, 419, 493, 573, 659, 751, 849, 953, 1063, 1179, 1301, 1429, 1563, 1703, 1849, 2001, 2159, 2323, 2493, 2669, 2851, 3039, 3233, 3433, 3639, 3851, 4069, 4293, 4523, 4759, 5001, 5249, 5503, 5763, 6029, 6301, 6579

Offset

1,2

Comments

Sequence's original Name was "First bisection of A135370."

The partial sums of this sequence give A081437. - Leo Tavares, Dec 26 2021

Links

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

John Elias, Illustration: Belted Hexagrams

Leo Tavares, Illustration: Bounded Hexagons

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

Formula

a(n+1) = a(n) + 6*n + 2; see A016933.

G.f.: x*(1+6*x-x^2)/(1-x)^3. a(n) = A049450(n)-1. - R. J. Mathar, Oct 24 2008

a(-n) = A144391(n). - Michael Somos, Mar 27 2014

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

From Leo Tavares, Dec 26 2021: (Start)

a(n) = A003215(n) - 2*A005408(n). See Bounded Hexagons illustration.

a(n) = A016754(n-1) - A002378(n-2). (End)

a(n) = A003154(n) - A049451(n-1). - John Elias, Dec 22 2022

Maple

A144390:=n->3*n^2-n-1; seq(A144390(n), n=1..50); # Wesley Ivan Hurt, Mar 26 2014

Mathematica

Table[3*n^2 -n -1 , {n, 0, 50}] (* G. C. Greubel, Jul 19 2017 *)

Prog

(Magma) [3*n^2-n-1: n in [1..60]]; // Vincenzo Librandi, Jun 14 2011
(PARI) a(n)=3*n^2-n-1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A016933, A049450, A144391.

Cf. A003215, A005408, A016754, A002378.

Cf. A081437 (partial sums).

Sequence in context: A054302 A147395 A302906 * A024843 A363161 A183453

Adjacent sequences: A144387 A144388 A144389 * A144391 A144392 A144393

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, Oct 25 2008

Status

approved