OFFSET
0,2
COMMENTS
Polynomial expanded is constant*(x+1/2)^2*(1+2x)/(1-x-16x^2+16x^3) the Jasinski rational polynomial p[x_] = (9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)) f[x_] := 1/p[x] /; 0 <= x <= 1/2 f[x_] := p[x] /; 1/2 < x <= 1 gives a Farey like function with maximum at 1.
LINKS
Index entries for linear recurrences with constant coefficients, signature (-1,16,16).
FORMULA
b(n) = coefficient series expansion of (9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)) a(n) = (-16/9)*b(n).
a(n) = (5*(-4)^n+4*(-1)^n+81*4^n)/60 for n>0. G.f.: -(2*x+1)^3 / ((x+1)*(4*x-1)*(4*x+1)). [Colin Barker, Dec 03 2012]
a(n) = -a(n-1)+16*a(n-2)+16*a(n-3). - Wesley Ivan Hurt, May 07 2021
MATHEMATICA
b = -(16/9)*ReplacePart[Table[Coefficient[Series[(9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)), {x, 0, 30}], x^n], {n, 0, 30}], -9/16, 1]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Jan 31 2006
STATUS
approved