cp's OEIS Frontend

A275861 a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = 2 + sqrt(5), s = r/(r-1), c = 4, d = 1, a(0) = 1, a(1) = 1.

%I A275861 #17 Sep 08 2022 08:46:17
%S A275861 1,1,9,51,305,1813,10784,64144,381543,2269503,13499513,80298135,
%T A275861 477631347,2841058559,16899254596,100520563016,597918892325,
%U A275861 3556555903317,21155193548465,125835844069155,748499871500621,4452245397810113,26482955892270832
%N A275861 a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = 2 + sqrt(5), s = r/(r-1), c = 4, d = 1, a(0) = 1, a(1) = 1.
%H A275861 Clark Kimberling, <a href="/A275861/b275861.txt">Table of n, a(n) for n = 0..1000</a>
%H A275861 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,5,-3,-3,3,-1).
%F A275861 a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = 2 + sqrt(5), s = r/(r-1), c = 4, d = 1, a(0) = 1, a(1) = 1.
%F A275861 G.f.: (1 -6*x +9*x^2 -10*x^3 +9*x^4 -4*x^5)/(1 -7*x +7*x^2 -5*x^3 +3*x^4 +3*x^5 -3*x^6 +x^7).
%t A275861 c = 4; d = 1; z = 40;
%t A275861 r = (c + Sqrt[c^2 + 4 d])/2; s = r/(r - 1); a[0] = 1; a[1] = 1;
%t A275861 a[n_] := a[n] = Floor[c*s*a[n - 1]] + Floor[d*r*a[n - 2]];
%t A275861 t = Table[a[n], {n, 0, z}]
%t A275861 CoefficientList[Series[(1-6*x+9*x^2-10*x^3+9*x^4-4*x^5)/(1-7*x+7*x^2 -5*x^3+3*x^4+3*x^5-3*x^6+x^7), {x,0, 50}], x] (* _G. C. Greubel_, Feb 08 2018 *)
%t A275861 LinearRecurrence[{7,-7,5,-3,-3,3,-1},{1,1,9,51,305,1813,10784},40] (* _Harvey P. Dale_, Dec 21 2018 *)
%o A275861 (PARI) x='x+O('x^30); Vec((1-6*x+9*x^2-10*x^3+9*x^4-4*x^5)/(1-7*x+7*x^2 -5*x^3+3*x^4+3*x^5-3*x^6+x^7)) \\ _G. C. Greubel_, Feb 08 2018
%o A275861 (Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((1-6*x+9*x^2-10*x^3+9*x^4-4*x^5)/(1-7*x+7*x^2 -5*x^3+3*x^4+ 3*x^5- 3*x^6+x^7))) // _G. C. Greubel_, Feb 08 2018
%Y A275861 Cf. A275856, A275857, A275858, A275859, A275860.
%K A275861 nonn,easy
%O A275861 0,3
%A A275861 _Clark Kimberling_, Aug 12 2016