A337281 a(n) = n*T(n), where T(n) = A000073(n) = n-th tribonacci number.

0, 0, 2, 3, 8, 20, 42, 91, 192, 396, 810, 1639, 3288, 6552, 12978, 25575, 50176, 98056, 190962, 370747, 717800, 1386252, 2671130, 5136291, 9857856, 18886900, 36127962, 69005439, 131621560, 250735856, 477077730, 906732175, 1721538560, 3265353168, 6187918434, 11716102195, 22164965064, 41900163524

Offset: 0

Author

N. J. A. Sloane, Sep 12 2020

Keywords

• nonn

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).

Crossrefs

Cf. A000073.

Programs

Mathematica

LinearRecurrence[{2,1,0,-3,-2,-1},{0,0,2,3,8,20},40] (* Harvey P. Dale, Dec 19 2023 *)

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

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)