A173187 a(n) = binomial(n + 3, 3)*9^n.

1, 36, 810, 14580, 229635, 3306744, 44641044, 573956280, 7102708965, 85232507580, 997220338686, 11422705697676, 128505439098855, 1423444863864240, 15556218869373480, 168007163789233584

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (36,-486,2916,-6561).

Formula

From Harvey P. Dale, May 19 2011: (Start)

a(n) = 36*a(n-1)-486*a(n-2)+ 2916*a(n-3)-6561*a(n-4).

G.f.: 1/(1-9*x)^4. (End)

From Amiram Eldar, Aug 28 2022: (Start)

Sum_{n>=0} 1/a(n) = 1728*log(9/8) - 405/2.

Sum_{n>=0} (-1)^n/a(n) = 2700*log(10/9) - 567/2. (End)

Maple

A173187:=n->binomial(n+3, 3)*9^n: seq(A173187(n), n=0..30); # Wesley Ivan Hurt, Jul 24 2017

Mathematica

Table[Binomial[n + 3, 3]*9^n, {n, 0, 20}]
LinearRecurrence[{36, -486, 2916, -6561}, {1, 36, 810, 14580}, 30] (* Harvey P. Dale, May 19 2011 *)

Prog

(Magma) [Binomial(n+3, 3)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011
(PARI) a(n)=binomial(n+3, 3)*9^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A081139, A173000.

Sequence in context: A110206 A133051 A215605 * A028222 A028216 A028221

Adjacent sequences: A173184 A173185 A173186 * A173188 A173189 A173190

Keyword

nonn,easy

Author

Zerinvary Lajos, Feb 12 2010

Status

approved