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A099464 Trisection of tribonacci numbers. 4


%S 0,1,7,44,274,1705,10609,66012,410744,2555757,15902591,98950096,

%T 615693474,3831006429,23837527729,148323355432,922906855808,

%U 5742568741225,35731770264967,222332455004452,1383410902447554,8607945812375585,53560898629395777,333269972246340068

%N Trisection of tribonacci numbers.

%C Let A = [1,1,1; 2,4,3; 1,2,2]. a(n) is given by the (1,2) term in A^n.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-5,1).

%F G.f.: x/(1-7*x+5*x^2-x^3).

%F a(n) = 7a(n-1) -5a(n-2) +a(n-3).

%F a(n) = A000073(3n).

%F a(n) = Sum_{i>=n-1} A120987(i,n-1) for n>0. - _Alois P. Heinz_, Dec 11 2015

%p a:= n-> (<<0|1|0>, <0|0|1>, <1|-5|7>>^n)[3, 1]:

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Dec 11 2015

%t LinearRecurrence[{7,-5,1},{0,1,7},30] (* _Harvey P. Dale_, Jan 14 2016 *)

%Y Cf. A009943, A120987.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Oct 16 2004

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Last modified December 11 02:24 EST 2019. Contains 329910 sequences. (Running on oeis4.)