OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,8,-8).
FORMULA
a(n) = 9*8^((n-1)/2)-2 (n odd), 2*8^(n/2)-2 (n even).
G.f.: 7*x*(x+1) / ((x-1)*(8*x^2-1)). - Colin Barker, Feb 15 2013
From G. C. Greubel, Oct 27 2016: (Start)
a(n) = a(n-1) + 8*a(n-2) - 8*a(n-3).
a(n) = (1/(4*sqrt(2)))*( -8*sqrt(2) + 9*(1 - (-1)^n)*2^(3*n/2) + (1 + (-1)^n)*2^((3*n+5)/2) ).
E.g.f.: 2*cosh(2*sqrt(2)*x) + (9/(2*sqrt(2)))*sinh(2*sqrt(2)*x) -2*cosh(x) - 2*sinh(x). (End)
MATHEMATICA
Table[If[OddQ[n], 9*8^((n-1)/2)-2, 2*8^(n/2)-2], {n, 1, 25}] (* or *) LinearRecurrence[{1, 8, -8}, {7, 14, 70}, 25] (* G. C. Greubel, Oct 27 2016 *)
Rest@ CoefficientList[Series[7 x (x + 1)/((x - 1) (8 x^2 - 1)), {x, 0, 27}], x] (* Michael De Vlieger, Oct 27 2016 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Martin Renner, May 02 2006
EXTENSIONS
More terms from Colin Barker, Feb 15 2013
STATUS
approved