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A073748 a(n) = S(n)*S(n-1), where S(n) are the generalized tribonacci numbers A001644.

%I A073748 #19 Sep 08 2022 08:45:06
%S A073748 -3,3,3,21,77,231,819,2769,9301,31571,106763,361045,1221685,4132743,
%T A073748 13980747,47297217,160004685,541291715,1831178355,6194830005,
%U A073748 20956959933,70896891079,239842458947,811381229009,2744883043045,9285872805715,31413882695739,106272403946805
%N A073748 a(n) = S(n)*S(n-1), where S(n) are the generalized tribonacci numbers A001644.
%H A073748 G. C. Greubel, <a href="/A073748/b073748.txt">Table of n, a(n) for n = 0..1000</a>
%H A073748 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 3, 6, -1, 0, -1).
%F A073748 a(n) = S(2*n-1) + C(n-1) - C(n-2), where S(n) is A001644, C(n) is A073145.
%F A073748 G.f.: (-3 + 9*x + 6*x^2 + 24*x^3 + 5*x^4 - x^5)/(1 - 2*x - 3*x^2 - 6*x^3 + x^4 + x^6).
%F A073748 a(0)=-3, a(1)=3, a(2)=3, a(3)=21, a(4)=77, a(5)=231, a(n) = 2*a(n-1) + 3*a(n-2) + 6*a(n-3) - a(n-4) - a(n-6). - _Harvey P. Dale_, Nov 18 2013
%t A073748 CoefficientList[Series[(-3+9*x+6*x^2+24*x^3+5*x^4-x^5)/(1-2*x-3*x^2-6*x^3 +x^4+x^6), {x, 0, 30}], x]
%t A073748 Join[{-3},Times@@@Partition[LinearRecurrence[{1,1,1},{3,1,3},30],2,1]] (* or *) LinearRecurrence[{2,3,6,-1,0,-1},{-3,3,3,21,77,231},30] (* _Harvey P. Dale_, Nov 18 2013 *)
%o A073748 (PARI) my(x='x+O('x^30)); Vec((-3+9*x+6*x^2+24*x^3+5*x^4-x^5)/(1-2*x-3*x^2-6*x^3 +x^4+x^6)) \\ _G. C. Greubel_, Apr 21 2019
%o A073748 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (-3+9*x+6*x^2+24*x^3+5*x^4-x^5)/(1-2*x-3*x^2-6*x^3 +x^4+x^6) )); // _G. C. Greubel_, Apr 21 2019
%o A073748 (Sage) ((-3+9*x+6*x^2+24*x^3+5*x^4-x^5)/(1-2*x-3*x^2-6*x^3 +x^4+x^6)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 21 2019
%Y A073748 Cf. A001644, A073145.
%K A073748 easy,sign
%O A073748 0,1
%A A073748 Maio Catalani (mario.catalani(AT)unito.it), Aug 08 2002