A193872 Even dodecagonal numbers: a(n) = 4*n*(5*n - 2).

0, 12, 64, 156, 288, 460, 672, 924, 1216, 1548, 1920, 2332, 2784, 3276, 3808, 4380, 4992, 5644, 6336, 7068, 7840, 8652, 9504, 10396, 11328, 12300, 13312, 14364, 15456, 16588, 17760, 18972, 20224, 21516, 22848, 24220, 25632, 27084, 28576, 30108, 31680, 33292, 34944

Offset: 0

Author

Omar E. Pol, Aug 19 2011

Keywords

• nonn
• easy

Comments

Even 12-gonal numbers. Bisection of A051624.

Links

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

Crossrefs

Cf. A016885, A051624, A147874.

Programs

Mathematica

PolygonalNumber[12,2*Range[0,40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 02 2017 *)

PARI

a(n)=4*n*(5*n-2) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 4*A147874(n+1).

a(n) = 4*n*A016885(n-1), n >= 1.

From Elmo R. Oliveira, Dec 15 2024: (Start)

G.f.: 4*x*(3 + 7*x)/(1 - x)^3.

E.g.f.: 4*x*(3 + 5*x)*exp(x).

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