OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,0,-5,0,3,1).
FORMULA
From Colin Barker, Jun 29 2015: (Start)
a(n) = 3*a(n-1) - 5*a(n-3) + 3*a(n-5) + a(n-6).
G.f.: -x*(x^4 - x^3 + 6*x^2 + x + 1)/(x^2 + x - 1)^3. (End)
E.g.f.: exp(x/2)*x*(sqrt(5)*(1 + x)*cosh(sqrt(5)*x/2) + (1 + 3*x)*sinh(sqrt(5)*x/2))/sqrt(5). - Stefano Spezia, Mar 04 2023
MAPLE
a:= n-> n^2*(<<1|1>, <1|0>>^n)[1, 2]:
seq(a(n), n=0..50); # Alois P. Heinz, Jun 30 2015
MATHEMATICA
a[n_] := n^2 MatrixPower[{{1, 1}, {1, 0}}, n][[1, 2]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 14 2016, after Alois P. Heinz *)
PROG
(PARI) concat(0, Vec(-x*(x^4-x^3+6*x^2+x+1)/(x^2+x-1)^3 + O(x^100))) \\ Colin Barker, Jun 29 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 27 2015
STATUS
approved