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A132804
A trisection of A024495.
6
0, 6, 42, 342, 2730, 21846, 174762, 1398102, 11184810, 89478486, 715827882, 5726623062, 45812984490, 366503875926, 2932031007402, 23456248059222, 187649984473770, 1501199875790166, 12009599006321322, 96076792050570582, 768614336404564650
OFFSET
0,2
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) = A078008(3n+1). Second trisection of A078008.
a(n) = 6*A015565(n).
a(n) = Sum_{k=0..n} binomial(3*n+1,3*k+2). (End)
MAPLE
A132804:=n->-(2/3)*(-1)^n+(2/3)*8^n: seq(A132804(n), n=0..30); # Wesley Ivan Hurt, Apr 14 2017
MATHEMATICA
LinearRecurrence[{7, 8}, {0, 6}, 30] (* Harvey P. Dale, Mar 29 2018 *)
PROG
(Magma) [-(2/3)*(-1)^n+(2/3)*8^n: n in [0..25]]; // Vincenzo Librandi, Jun 08 2011
(PARI) a(n)=2*(8^n-(-1)^n)/3 \\ Charles R Greathouse IV, Jun 08 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 18 2007
STATUS
approved