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A163306 a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

%I A163306 #8 Sep 08 2022 08:45:46
%S A163306 1,7,53,419,3385,27631,226637,1863083,15331249,126219415,1039364261,
%T A163306 8559569267,70494539113,580587822079,4781723152445,39382455344891,
%U A163306 324356046412897,2671416441263143,22001959856357909,181209608597137475
%N A163306 a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
%C A163306 Binomial transform of A090041. Inverse binomial transform of A163307.
%H A163306 G. C. Greubel, <a href="/A163306/b163306.txt">Table of n, a(n) for n = 0..1000</a>
%H A163306 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-31).
%F A163306 a(n) = ((5+sqrt(5))*(6+sqrt(5))^n + (5-sqrt(5))*(6-sqrt(5))^n)/10.
%F A163306 G.f.: (1-5*x)/(1-12*x+31*x^2).
%F A163306 E.g.f.: (1/5)*exp(6*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - _G. C. Greubel_, Dec 18 2016
%t A163306 LinearRecurrence[{12,-31}, {1,7}, 50] (* _G. C. Greubel_, Dec 18 2016 *)
%o A163306 (Magma) [ n le 2 select 6*n-5 else 12*Self(n-1)-31*Self(n-2): n in [1..20] ];
%o A163306 (PARI) Vec((1-5*x)/(1-12*x+31*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 18 2016
%Y A163306 Cf. A090041, A163307.
%K A163306 nonn,easy
%O A163306 0,2
%A A163306 _Klaus Brockhaus_, Jul 24 2009