A152965 Twice 12-gonal numbers: a(n) = 2*n*(5*n-4).

0, 2, 24, 66, 128, 210, 312, 434, 576, 738, 920, 1122, 1344, 1586, 1848, 2130, 2432, 2754, 3096, 3458, 3840, 4242, 4664, 5106, 5568, 6050, 6552, 7074, 7616, 8178, 8760, 9362, 9984, 10626, 11288, 11970, 12672, 13394, 14136, 14898, 15680, 16482, 17304, 18146, 19008

Offset: 0

Author

Omar E. Pol, Dec 21 2008

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A051624 (12-gonal numbers), A051874.

Cf. numbers of the form n*(n*k - k + 4)/2 listed in A226488 (this sequence is the case k=20). - Bruno Berselli, Jun 10 2013

Programs

Magma

[10*n^2-8*n: n in [0..50]]; // Klaus Brockhaus, Nov 27 2010

Mathematica

Table[10*n^2-8*n,{n,0,50}] (* Vincenzo Librandi, Jul 10 2012 *)
LinearRecurrence[{3,-3,1},{0,2,24},60] (* Harvey P. Dale, Apr 18 2016 *)

PARI

a(n)=2*n*(5*n-4) \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 2*A051624(n).

From Vincenzo Librandi, Jul 10 2012: (Start)

G.f.: 2*x*(1+9*x)/(1-x)^3.

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

From Elmo R. Oliveira, Dec 27 2024: (Start)

E.g.f.: 2*exp(x)*x*(1 + 5*x).

a(n) = n + A051874(n). (End)