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A163307 a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

%I A163307 #10 Sep 08 2022 08:45:46
%S A163307 1,8,68,600,5408,49312,452416,4164096,38391040,354254336,3270354944,
%T A163307 30197778432,278873280512,2575523676160,23786907123712,
%U A163307 219693657980928,2029087298289664,18740701224894464,173089976023777280
%N A163307 a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
%C A163307 Binomial transform of A163306. Inverse binomial transform of A163308.
%H A163307 G. C. Greubel, <a href="/A163307/b163307.txt">Table of n, a(n) for n = 0..1000</a>
%H A163307 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-44).
%F A163307 a(n) = ((5+sqrt(5))*(7+sqrt(5))^n + (5-sqrt(5))*(7-sqrt(5))^n)/10.
%F A163307 G.f.: (1-6*x)/(1-14*x+44*x^2).
%F A163307 E.g.f.: (1/5)*exp(7*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - _G. C. Greubel_, Dec 18 2016
%t A163307 LinearRecurrence[{14,-44}, {1,8}, 50] (* _G. C. Greubel_, Dec 18 2016 *)
%o A163307 (Magma) [ n le 2 select 7*n-6 else 14*Self(n-1)-44*Self(n-2): n in [1..19] ];
%o A163307 (PARI) Vec((1-6*x)/(1-14*x+44*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 18 2016
%Y A163307 Cf. A163306, A163308.
%K A163307 nonn
%O A163307 0,2
%A A163307 _Klaus Brockhaus_, Jul 24 2009