A104188 a(n) = 4*n*(4*n - 1).

0, 12, 56, 132, 240, 380, 552, 756, 992, 1260, 1560, 1892, 2256, 2652, 3080, 3540, 4032, 4556, 5112, 5700, 6320, 6972, 7656, 8372, 9120, 9900, 10712, 11556, 12432, 13340, 14280, 15252, 16256, 17292, 18360, 19460, 20592, 21756, 22952, 24180, 25440, 26732, 28056, 29412, 30800

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = (4*n)!/(4*n-2)! for n>0.

a(n) = 32*n + a(n-1) - 20 (with a(0)=0). - Vincenzo Librandi, Nov 13 2010

From Colin Barker, Jun 25 2012: (Start)

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

G.f.: 4*x*(3+5*x)/(1-x)^3. (End)

Sum_{n>=1} 1/a(n) = 3*log(2)/4 - Pi/8. - Amiram Eldar, Jan 03 2022

E.g.f.: 4*exp(x)*x*(3 + 4*x). - Stefano Spezia, Nov 29 2024

Example

a(2) = (4*2)!/(4*2-2)! = 8!/6! = 8*7 = 56.

Maple

for n from 1 to 100 do printf(`%d, `, (4*n-4)*(4*n-5)) od: # James Sellers, Apr 10 2005

Mathematica

A104188[n_] := 4*n*(4*n - 1); Array[A104188, 50, 0] (* or *)
LinearRecurrence[{3, -3, 1}, {0, 12, 56}, 50] (* Paolo Xausa, Mar 12 2026 *)

Prog

(PARI) a(n)=4*n*(4*n-1) \\ Charles R Greathouse IV, Jun 16 2017

Crossrefs

Cf. A004767, A008586.

Sequence in context: A009653 A133001 A340517 * A389478 A069552 A035005

Adjacent sequences: A104185 A104186 A104187 * A104189 A104190 A104191

Keyword

nonn,easy

Author

Ruppi Rana (ruppi.rana(AT)gmail.com), Mar 12 2005

Extensions

More terms from James Sellers, Apr 10 2005

Simpler definition from Ralf Stephan, May 20 2007

More terms from Paolo Xausa, Mar 12 2026

Status

approved