A083334 a(n) = 12*a(n-2) - 25*a(n-4) with initial terms 1,6,17,47.
1, 6, 17, 47, 179, 414, 1723, 3793, 16201, 35166, 151337, 327167, 1411019, 3046854, 13148803, 28383073, 122510161, 264425526, 1141401857, 2463529487, 10634068259, 22951715694, 99073772683, 213832351153, 923033565721
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,12,0,-25).
Programs
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Mathematica
CoefficientList[Series[(1+6x+5x^2-25x^3)/(1-12x^2+25x^4), {x, 0, 10}], x] LinearRecurrence[{0,12,0,-25},{1,6,17,47},30] (* Harvey P. Dale, Oct 15 2012 *)
Formula
G.f.: (1 + 6*x + 5*x^2 - 25*x^3) / (1 - 12*x^2 + 25*x^4).
a(n) = (x^(n+1) + (-1)^(n+1)*(x-2)^(n+1))/2^ceiling(n/2 + 1) where x = 1 + sqrt(11). - Ben Paul Thurston, Aug 30 2006 [edited by Jon E. Schoenfield, Jun 25 2019]
Comments