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

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

There is a ball-hating monster that lives in a box. You throw 4 numbered balls into the box. He throws 2 balls out. Repeat. Then a(n) gives the number of ordered possibilities the monster has to throw the balls back at each stage (2,1 is different from 1,2).

Examples

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

Links

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

Crossrefs

Cf. A004767, A008586.

Programs

Maple

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

PARI

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

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

Extensions

More terms from James Sellers, Apr 10 2005

Simpler definition from Ralf Stephan, May 20 2007