A152995 Twice 11-gonal numbers: a(n) = n*(9*n-7).

0, 2, 22, 60, 116, 190, 282, 392, 520, 666, 830, 1012, 1212, 1430, 1666, 1920, 2192, 2482, 2790, 3116, 3460, 3822, 4202, 4600, 5016, 5450, 5902, 6372, 6860, 7366, 7890, 8432, 8992, 9570, 10166, 10780, 11412, 12062, 12730, 13416, 14120

Offset: 0

Author

Omar E. Pol, Dec 22 2008

Keywords

• easy
• nonn

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. A051682 (11-gonal numbers).

Cf. A226488.

Programs

GAP

List([0..50], n-> n*(9*n-7)); # G. C. Greubel, Sep 01 2019

Magma

[n*(9*n-7): n in [0..50]];

Maple

seq(n*(9*n-7), n=0..50); # G. C. Greubel, Sep 01 2019

Mathematica

Table[n(9n-7),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,2,22},40] (* Harvey P. Dale, Nov 02 2011 *)
2*PolygonalNumber[11,Range[0,40]] (* Harvey P. Dale, May 31 2024 *)

PARI

a(n)=n*(9*n-7) \\ Charles R Greathouse IV, Jun 17 2017

Sage

[n*(9*n-7) for n in (0..50)] # G. C. Greubel, Sep 01 2019

Formula

a(n) = 9*n^2 - 7*n = A051682(n)*2.

a(n) = a(n-1) + 18*n - 16 (with a(0)=0). - Vincenzo Librandi, Nov 27 2010

a(0)=0, a(1)=2, a(2)=22, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Nov 02 2011

From G. C. Greubel, Sep 01 2019: (Start)

G.f.: 2*x*(1+8*x)/(1-x)^3.

E.g.f.: x*(2+9*x)*exp(x). (End)