%I #24 Jan 01 2024 11:27:29
%S 1,15,141,1443,14505,146343,1475349,14875995,149990289,1512318207,
%T 15248341725,153745416147,1550178505401,15630081782295,
%U 157594402871781,1588986940402443,16021377983526945,161539749616666863,1628766934587400749,16422470218649210115
%N a(n) = 8*a(n-1) + 21*a(n-2), with a(1)=1, a(2)=15.
%H G. C. Greubel, <a href="/A093117/b093117.txt">Table of n, a(n) for n = 1..990</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,21).
%F Limit_{n -> oo} a(n+1)/a(n) converges to 4 + sqrt(37).
%F G.f.: x*(1+7*x)/(1-8*x-21*x^2). - _Stefan Steinerberger_, Nov 18 2005
%F a(n) = A093103(n) + 7*A093103(n-1). - _G. C. Greubel_, Feb 10 2023
%t LinearRecurrence[{8,21},{1,15},20] (* _Harvey P. Dale_, Nov 03 2020 *)
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+7*x)/(1-8*x-21*x^2) )); // _G. C. Greubel_, Feb 09 2023
%o (SageMath)
%o @CachedFunction
%o def b(n): # b = A093103
%o if (n<3): return (0,1,8)[n]
%o else: return 8*b(n-1) + 21*b(n-2)
%o def A093117(n): return b(n) + 7*b(n-1)
%o [A093117(n) for n in range(1, 41)] # _G. C. Greubel_, Feb 09 2023
%Y Cf. A093103, A094703.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, May 21 2004
%E More terms from _Robert G. Wilson v_, May 24 2004
%E Edited by _Don Reble_, Nov 04 2005