A132804 A trisection of A024495.
0, 6, 42, 342, 2730, 21846, 174762, 1398102, 11184810, 89478486, 715827882, 5726623062, 45812984490, 366503875926, 2932031007402, 23456248059222, 187649984473770, 1501199875790166, 12009599006321322, 96076792050570582, 768614336404564650
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (7,8).
Programs
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Magma
[-(2/3)*(-1)^n+(2/3)*8^n: n in [0..25]]; // Vincenzo Librandi, Jun 08 2011
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Maple
A132804:=n->-(2/3)*(-1)^n+(2/3)*8^n: seq(A132804(n), n=0..30); # Wesley Ivan Hurt, Apr 14 2017
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Mathematica
LinearRecurrence[{7,8},{0,6},30] (* Harvey P. Dale, Mar 29 2018 *) -
PARI
a(n)=2*(8^n-(-1)^n)/3 \\ Charles R Greathouse IV, Jun 08 2011
Formula
G.f.: 6*x/(1-7*x-8*x^2). a(n+1) = 7*a(n)+8*a(n-1) for n>=1, a(0)=0, a(1)=6. - Philippe Deléham, Nov 19 2007
a(n) = 2*A132805(n). - R. J. Mathar, Jun 07 2011
From Oboifeng Dira, Jun 05 2020: (Start)
a(n) = 6*A015565(n).
a(n) = Sum_{k=0..n} binomial(3*n+1,3*k+2). (End)