OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Physics Forums, How to approximate the rate of growth of an integer sequence? [Contains the sequence of numbers, but not the g.f., which was found by Alexander R. Povolotsky]
Index entries for linear recurrences with constant coefficients, signature (8,-21,22,-8).
FORMULA
From G. C. Greubel, Feb 26 2017: (Start)
a(n) = 8*a(n-1) - 21*a(n-2) + 22*a(n-3) - 8*a(n-4).
a(n) = (1/12)*(68 + 49*2^(2*n+2) - 63*2^(2 + n) + 12*n).
E.g.f.: (1/12)*(196*exp(4*x) - 252*exp(2*x) + 4*(17 + 3*x)*exp(x)). (End)
MATHEMATICA
CoefficientList[Series[(1 + 22 *x - 34* x^2 + 14 *x^3)/((1 - x)^2 *(1 - 6* x + 8* x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 26 2017 *)
PROG
(PARI) x='x+O('x^50); Vec((1 + 22*x - 34*x^2 + 14*x^3)/((1 - x)^2*(1 - 6*x + 8*x^2))) \\ G. C. Greubel, Feb 26 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 2015, based on a suggestion from Alexander R. Povolotsky
STATUS
approved