A275778 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) = 1.

1, 2, 1, 4, 7, 12, 23, 42, 77, 142, 261, 480, 883, 1624, 2987, 5494, 10105, 18586, 34185, 62876, 115647, 212708, 391231, 719586, 1323525, 2434342, 4477453, 8235320, 15147115, 27859888, 51242323, 94249326, 173351537, 318843186, 586444049

Offset: 0

Author

Nicolas Bègue, Sep 10 2016

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000073, A276658.

Programs

Mathematica

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

PARI

a(n)=([0,1,0; 0,0,1; 1,1,1]^n*[1;2;1])[1,1] \\ Charles R Greathouse IV, Sep 10 2016

Formula

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

a(n) = A276658(n) + A000073(n).