%I #62 May 31 2020 00:53:21

%S 1,2,1,4,7,12,23,42,77,142,261,480,883,1624,2987,5494,10105,18586,

%T 34185,62876,115647,212708,391231,719586,1323525,2434342,4477453,

%U 8235320,15147115,27859888,51242323,94249326,173351537,318843186,586444049

%N 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.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).

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

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

%t CoefficientList[Series[(-1 - x + 2 x^2)/(-1 + x + x^2 + x^3), {x, 0, 35}], x]

%t RecurrenceTable[{a[n] == a[n - 1] + a[n - 2] + a[n - 3], a[1] == 1, a[2] == 2, a[3] == 1}, a, {n, 35}]

%t LinearRecurrence[{1, 1, 1}, {1, 2, 1}, 35]

%o (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

%Y Cf. A000073, A276658.

%K nonn,easy

%O 0,2

%A _Nicolas Bègue_, Sep 10 2016