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

0,3

References

Raphael Schumacher, Explicit formulas for sums involving the squares of the first n Tribonacci numbers, Fib. Q., 58:3 (2020), 194-202.

Links

Table of n, a(n) for n=0..37.

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

Cf. A000073.

Sequence in context: A042697 A042905 A247568 * A092031 A082914 A333680

Adjacent sequences: A337278 A337279 A337280 * A337282 A337283 A337284

Keyword

nonn

Author

N. J. A. Sloane, Sep 12 2020

Status

approved