OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10, -40, 82, -91, 52, -12).
FORMULA
a(n) = 3*a(n-1)+ (n+3)*(2^(n+2)-(n+3)), n>=1, a(0)=3.
G.f.: (3-5*x)/(((1-x)^3)*((1-2*x)^2)*(1-3*x)).
a(n) = 3^(n+4)/2 - (n+6)*2^(n+3) + n^2/2 + 9*n/2 + 21/2. - Vaclav Kotesovec, Jul 23 2021
MATHEMATICA
CoefficientList[Series[(3 - 5*x)/(((1 - x)^3)*((1 - 2*x)^2)*(1 - 3*x)), {x, 0, 50}], x] (* G. C. Greubel, Nov 13 2017 *)
Table[3^(n+4)/2 - (n+6)*2^(n+3) + n^2/2 + 9*n/2 + 21/2, {n, 0, 25}] (* Vaclav Kotesovec, Jul 23 2021 *)
PROG
(PARI) x='x+O('x^50); Vec((3-5*x)/(((1-x)^3)*((1-2*x)^2)*(1-3*x))) \\ G. C. Greubel, Nov 13 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 14 2005
STATUS
approved