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
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).
Programs
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Magma
[Binomial(n+3, 3)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011
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Maple
A173187:=n->binomial(n+3,3)*9^n: seq(A173187(n), n=0..30); # Wesley Ivan Hurt, Jul 24 2017
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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 *) -
PARI
a(n)=binomial(n+3,3)*9^n \\ Charles R Greathouse IV, Oct 07 2015
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)