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A090409
a(n) = (7*8^n + 2*(-1)^n)/9.
2
1, 6, 50, 398, 3186, 25486, 203890, 1631118, 13048946, 104391566, 835132530, 6681060238, 53448481906, 427587855246, 3420702841970, 27365622735758, 218924981886066, 1751399855088526, 14011198840708210, 112089590725665678, 896716725805325426, 7173733806442603406
OFFSET
0,2
FORMULA
a(n) = Sum_{j=0..2} Sum_{k=0..n} C(3*n+j, 3*k)/3.
a(n) = (A007613(n) + A082311(n) + A082365(n))/3.
G.f.: (-1+x)/((1+x)*(8*x-1)). - R. J. Mathar, Dec 10 2014
From Elmo R. Oliveira, Aug 18 2024: (Start)
E.g.f.: exp(-x)*(7*exp(9*x) + 2)/9.
a(n) = 7*a(n-1) + 8*a(n-2) for n > 1. (End)
MATHEMATICA
LinearRecurrence[{7, 8}, {1, 6}, 20] (* Harvey P. Dale, Aug 15 2016 *)
CROSSREFS
First differences of A015565.
Sequence in context: A308860 A318162 A027330 * A212233 A180910 A199680
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 29 2003
EXTENSIONS
a(20)-a(21) from Elmo R. Oliveira, Aug 18 2024
STATUS
approved