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

Author

Paul Curtz, Oct 02 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A016933, A049450, A144391.

Cf. A003215, A005408, A016754, A002378.

Cf. A081437 (partial sums).

Programs

Magma

[3*n^2-n-1: n in [1..60]]; // Vincenzo Librandi, Jun 14 2011

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 *)

PARI

a(n)=3*n^2-n-1 \\ Charles R Greathouse IV, Oct 07 2015

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

Extensions

Edited by R. J. Mathar, Oct 24 2008

More terms from Vladimir Joseph Stephan Orlovsky, Oct 25 2008