A166157 a(n) = (8^n+16*(-9)^n)/17.
1, -8, 80, -656, 6416, -53648, 515600, -4378256, 41501456, -356735888, 3344840720, -29029824656, 269858356496, -2360005731728, 21789807399440, -191710220083856, 1760576352843536, -15563712198881168
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-1, 72).
Programs
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Mathematica
LinearRecurrence[{-1,72},{1,-8},20] (* Harvey P. Dale, Jun 23 2012 *) -
PARI
a(n)=(8^n+16*(-9)^n)/17 \\ Charles R Greathouse IV, May 02 2016
Formula
a(n) = 72*a(n-2)-a(n-1), a(0)= 1, a(1)= -8, for n>1.
G.f.: (1-7x)/(1+x-72*x^2).
a(n)= Sum_{k, 0<=k<=n} A112555(n,k)*(-9)^k.
E.g.f.: (1/17)*(exp(8*x) + 16*exp(-9*x)). - G. C. Greubel, May 01 2016