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A073357 Binomial transform of tribonacci numbers.

%I A073357 #23 May 07 2017 22:44:04
%S A073357 0,1,3,8,22,62,176,500,1420,4032,11448,32504,92288,262032,743984,
%T A073357 2112384,5997664,17029088,48350464,137280832,389779648,1106696192,
%U A073357 3142227840,8921685888
%N A073357 Binomial transform of tribonacci numbers.
%C A073357 For n-> infinity the ratio a(n)/a(n-1) approaches 1+c, where c is the real root of the cubic x^3-x^2-x-1=0; c=1.8392867...
%C A073357 a(n) = rightmost term of M^n *[100] where M = the 3X3 matrix [1 1 0 / 0 1 1 / 1 1 2]. Middle term of the vector = partial sums of A073357 through a(n-1). E.g., M^5*[1 0 0] = [18 34 62] where 62 = a(5) and 34 = partial sums of A073357 through a(4): 34 = 0+1+3+8+22. - _Gary W. Adamson_, Jul 24 2005
%D A073357 Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, 1995.
%H A073357 Harvey P. Dale, <a href="/A073357/b073357.txt">Table of n, a(n) for n = 0..1000</a>
%H A073357 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A073357 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H A073357 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, -4, 2).
%F A073357 a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3), a(0)=0, a(1)=1, a(2)=3.
%F A073357 Generating function A(x)=(x-x^2)/(1-4x+4x^2-2x^3).
%F A073357 a(n) = A115390(n+1) - A115390(n). - _R. J. Mathar_, Apr 16 2009
%t A073357 h[n_] := h[n]=4*h[n-1]-4*h[n-2]+2*h[n-3]; h[0]=0; h[1]=1; h[2]=3
%t A073357 LinearRecurrence[{4,-4,2},{0,1,3},30] (* _Harvey P. Dale_, Nov 13 2011 *)
%Y A073357 Cf. A000073, A073313. Trisection of A103685.
%K A073357 easy,nonn
%O A073357 0,3
%A A073357 Mario Catalani (mario.catalani(AT)unito.it), Jul 29 2002