cp's OEIS Frontend

A117189 Binomial transform of the tribonacci sequence A000073 (shifted left twice).

%I A117189 #30 Jan 04 2023 12:15:17
%S A117189 1,2,5,14,40,114,324,920,2612,7416,21056,59784,169744,481952,1368400,
%T A117189 3885280,11031424,31321376,88930368,252498816,716916544,2035531648,
%U A117189 5779458048,16409538688,46591385856,132286304768,375598753024,1066432564736,3027907856384
%N A117189 Binomial transform of the tribonacci sequence A000073 (shifted left twice).
%C A117189 a(n)/a(n-1) tends to 2.83928675... = A058265 + 1.
%C A117189 Partial sums are in A073357. - _R. J. Mathar_, Apr 02 2008
%H A117189 Vincenzo Librandi, <a href="/A117189/b117189.txt">Table of n, a(n) for n = 0..1000</a>
%H A117189 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,2).
%F A117189 Binomial transform of A000073 starting with A000073(2): (1, 1, 2, 4, 7, 13, ...).
%F A117189 a(n) = 4*a(n-1)-4*a(n-2)+2*a(n-3), n>2. - _T. D. Noe_, Nov 07 2006
%F A117189 O.g.f.: -(x-1)^2/(-1+4*x-4*x^2+2*x^3). - _R. J. Mathar_, Apr 02 2008
%F A117189 a(n) = 2*a(n-1) + Sum_{j=1..n-1} j*a(n-j-1), n>=1; with a(0) = 1. - _Bob Selcoe_, Jun 28 2014
%e A117189 a(4) = 14 = 1*1 + 3*1 + 3*2 + 1*4;
%e A117189 a(6) = 324 = 2*114 + 1*40 + 2*14 + 3*5 + 4*2 + 5*1. - _Bob Selcoe_, Jun 28 2014
%t A117189 CoefficientList[Series[-(x - 1)^2/(-1 + 4*x - 4*x^2 + 2*x^3), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jul 05 2014 *)
%t A117189 LinearRecurrence[{4,-4,2},{1,2,5},40] (* _Harvey P. Dale_, Oct 10 2016 *)
%Y A117189 Cf. A000073, A115390.
%K A117189 nonn
%O A117189 0,2
%A A117189 _Gary W. Adamson_, Mar 01 2006
%E A117189 Corrected and extended by _T. D. Noe_, Nov 07 2006