OFFSET
0,3
REFERENCES
Raphael Schumacher, Explicit formulas for sums involving the squares of the first n Tribonacci numbers, Fib. Q., 58:3 (2020), 194-202.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,1,0,-3,-2,-1).
FORMULA
From Colin Barker, Sep 13 2020: (Start)
G.f.: x^2*(2 - x + x^3) / (1 - x - x^2 - x^3)^2.
a(n) = 2*a(n-1) + a(n-2) - 3*a(n-4) - 2*a(n-5) - a(n-6) for n>5.
(End)
MATHEMATICA
LinearRecurrence[{2, 1, 0, -3, -2, -1}, {0, 0, 2, 3, 8, 20}, 40] (* Harvey P. Dale, Dec 19 2023 *)
PROG
(PARI) a(n)= n * ([0, 1, 0; 0, 0, 1; 1, 1, 1]^n)[1, 3] \\ David A. Corneth, Sep 13 2020, after Charles R Greathouse IV
(PARI) concat([0, 0], Vec(x^2*(2 - x + x^3) / (1 - x - x^2 - x^3)^2 + O(x^36))) \\ Colin Barker, Sep 13 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 12 2020
STATUS
approved