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A337281
a(n) = n*T(n), where T(n) = A000073(n) = n-th tribonacci number.
1
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.
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 12 2020
STATUS
approved