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%I #24 Jan 01 2024 11:27:33
%S 1,11,109,1103,11113,112067,1129909,11392679,114869521,1158202427,
%T 11677879357,117745285823,1187197753081,11970233026931,
%U 120693017030149,1216919029806743,12269905596087073,123714544394638187,1247384372674934029,12577080413686874159
%N a(n) = 8*a(n-1) + 21*a(n-2), with a(1)=1, a(2)=11.
%H Colin Barker, <a href="/A094703/b094703.txt">Table of n, a(n) for n = 1..997</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+3*x)/(1-8*x-21*x^2). - _Colin Barker_, May 22 2015
%F a(n) = A093103(n+1) + 3*A093103(n). - _G. C. Greubel_, Feb 09 2023
%t LinearRecurrence[{8,21}, {1,11}, 41] (* _G. C. Greubel_, Feb 09 2023 *)
%o (PARI) Vec(x*(1+3*x)/(1-8*x-21*x^2) + O(x^40)) \\ _Colin Barker_, May 22 2015
%o (Magma) [n le 2 select 10*n-9 else 8*Self(n-1) +21*Self(n-2): n in [1..41]]; // _G. C. Greubel_, Feb 09 2023
%o (SageMath)
%o @CachedFunction
%o def a(n): # a = A094703
%o if (n<3): return 10*n-9
%o else: return 8*a(n-1) + 21*a(n-2)
%o [a(n) for n in range(1,41)] # _G. C. Greubel_, Feb 09 2023
%Y Cf. A093103, A093117.
%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
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