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A165405
a(n) = 6*a(n-2) - a(n-1), with a(0)=1, a(1)=3.
3
1, 3, 3, 15, 3, 87, -69, 591, -1005, 4551, -10581, 37887, -101373, 328695, -936933, 2909103, -8530701, 25985319, -77169525, 233081439, -696098589, 2094587223, -6271178757, 18838702095, -56465774637, 169497987207, -508292635029, 1525280558271, -4575036368445
OFFSET
0,2
COMMENTS
a(n)/a(n-1) tends to -3.
FORMULA
G.f.: (1+4*x)/(1+x-6*x^2).
a(n) = Sum_{k=0..n} A112555(n,k)*2^k.
a(n) = (6*2^n - (-3)^n)/5. - Klaus Brockhaus, Sep 26 2009
E.g.f.: exp(-3*x)*(-1 + 6*exp(5*x))/5. - Elmo R. Oliveira, Feb 27 2026
MATHEMATICA
nxt[{a_, b_}]:={b, 6a-b}; NestList[nxt, {1, 3}, 30][[;; , 1]] (* or *) LinearRecurrence[{-1, 6}, {1, 3}, 30] (* Harvey P. Dale, May 24 2024 *)
CROSSREFS
Cf. A112555.
Sequence in context: A287100 A287188 A100347 * A179857 A260078 A163590
KEYWORD
sign,easy
AUTHOR
Philippe Deléham, Sep 17 2009
STATUS
approved