A139267 Twice octagonal numbers: 2*n*(3*n-2).

0, 2, 16, 42, 80, 130, 192, 266, 352, 450, 560, 682, 816, 962, 1120, 1290, 1472, 1666, 1872, 2090, 2320, 2562, 2816, 3082, 3360, 3650, 3952, 4266, 4592, 4930, 5280, 5642, 6016, 6402, 6800, 7210, 7632, 8066, 8512, 8970, 9440, 9922

Offset: 0

Author

Omar E. Pol, May 14 2008, May 19 2008

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 0, in the direction 0, 2,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A033580 in the same spiral. - Omar E. Pol, Sep 09 2011

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000567, A017545.

Cf. numbers of the form n*(n*k-k+4)/2 listed in A226488 (this sequence is the case k=12).

Programs

GAP

List([0..50], n-> 2*n*(3*n-2)); # G. C. Greubel, Sep 18 2019

Magma

[2*n*(3*n-2): n in [0..50]]; // G. C. Greubel, Sep 18 2019

Maple

seq(2*n*(3*n-2), n=0..50); # G. C. Greubel, Sep 18 2019

Mathematica

Table[2*n*(3*n-2), {n,0,50}] (* G. C. Greubel, Jun 07 2017 *)

PARI

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

Sage

[2*n*(3*n-2) for n in (0..50)] # G. C. Greubel, Sep 18 2019

Formula

a(n) = 2*A000567(n) = 6*n^2 - 4*n = 2*n*(3*n - 2).

a(n) = a(n-1) + 12*n - 10, with n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

G.f.: x*(2+10*x)/(1-3*x+3*x^2-x^3). - Colin Barker, Jan 06 2012

After 0, a(n) = Sum_{i=0..n-1} (12*i + 2). - Bruno Berselli, Sep 11 2013

E.g.f.: 2*x*(1 + 3*x)*exp(x). - G. C. Greubel, Sep 18 2019