A337282 Partial sums of A337281.

0, 0, 2, 5, 13, 33, 75, 166, 358, 754, 1564, 3203, 6491, 13043, 26021, 51596, 101772, 199828, 390790, 761537, 1479337, 2865589, 5536719, 10673010, 20530866, 39417766, 75545728, 144551167, 276172727, 526908583, 1003986313, 1910718488, 3632257048, 6897610216, 13085528650, 24801630845, 46966595909, 88866759433

Offset

0,3

References

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

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,-1,-3,1,1,1).

Formula

From Colin Barker, Sep 13 2020: (Start)

G.f.: x^2*(2 - x + x^3) / ((1 - x)*(1 - x - x^2 - x^3)^2).

a(n) = 3*a(n-1) - a(n-2) - a(n-3) - 3*a(n-4) + a(n-5) + a(n-6) + a(n-7) for n>6. (End)

Mathematica

LinearRecurrence[{3, -1, -1, -3, 1, 1, 1}, {0, 0, 2, 5, 13, 33, 75}, 40] (* Paolo Xausa, Jul 06 2026 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1; 1, 1, 1, -3, -1, -1, 3]^n*[0; 0; 2; 5; 13; 33; 75])[1, 1] \\ Charles R Greathouse IV, May 25 2026

Crossrefs

Cf. A000073, A337281.

Sequence in context: A108890 A220739 A396425 * A366117 A027929 A001659

Adjacent sequences: A337279 A337280 A337281 * A337283 A337284 A337285

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Sep 12 2020

Status

approved