A276658 Tribonacci-like sequence a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 3, with a(0) = 1, a(1) = 2, a(2) = 0.

1, 2, 0, 3, 5, 8, 16, 29, 53, 98, 180, 331, 609, 1120, 2060, 3789, 6969, 12818, 23576, 43363, 79757, 146696, 269816, 496269, 912781, 1678866, 3087916, 5679563, 10446345, 19213824, 35339732, 64999901, 119553457, 219893090

Offset

0,2

Links

Table of n, a(n) for n=0..33.

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

Formula

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

a(n) = A275778(n) - A000073(n).

Mathematica

LinearRecurrence[{1, 1, 1}, {1, 2, 0}, 35] (* or *)
RecurrenceTable[{a[n] == a[n - 1] + a[n - 2] + a[n - 3], a[1] == 1, a[2] == 2, a[3] == 0}, a, {n, 35}] (* or *)
CoefficientList[Series[(-1 - x + 3 x^2)/(-1 + x + x^2 + x^3), {x, 0, 40}], x]

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, 1, 1]^n*[1; 2; 0])[1, 1] \\ Charles R Greathouse IV, Sep 13 2016

Crossrefs

Cf. A000073, A275778.

Sequence in context: A094720 A334495 A155800 * A079510 A216255 A362788

Adjacent sequences: A276655 A276656 A276657 * A276659 A276660 A276661

Keyword

nonn,easy

Author

Nicolas Bègue, Sep 11 2016

Status

approved