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A164072 a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

%I A164072 #10 Sep 08 2022 08:45:47
%S A164072 1,7,42,238,1316,7196,39144,212408,1151248,6236272,33772704,182873824,
%T A164072 990172736,5361148352,29026768512,157158071168,850889810176,
%U A164072 4606905485056,24942786537984,135045615513088,731165912572928
%N A164072 a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
%C A164072 Binomial transform of A081179 without initial 0. Inverse binomial transform of A164031.
%H A164072 G. C. Greubel, <a href="/A164072/b164072.txt">Table of n, a(n) for n = 0..1000</a>
%H A164072 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-14).
%F A164072 a(n) = ((2+3*sqrt(2))*(4+sqrt(2))^n + (2-3*sqrt(2))*(4-sqrt(2))^n)/4.
%F A164072 G.f.: (1-x)/(1-8*x+14*x^2).
%F A164072 E.g.f.: (cosh(sqrt(2)*x) + (3*sqrt(2)/2)*sinh(sqrt(2)*x))*exp(4*x). - _G. C. Greubel_, Sep 09 2017
%t A164072 CoefficientList[Series[(1 - x)/(1 - 8*x + 14*x^2), {x,0,50}], x] (* or *) LinearRecurrence[{8,-14}, {1,7}, 50] (* _G. C. Greubel_, Sep 09 2017 *)
%o A164072 (Magma) [ n le 2 select 6*n-5 else 8*Self(n-1)-14*Self(n-2): n in [1..21] ];
%o A164072 (PARI) x='x+O('x^50); Vec((1-x)/(1-8*x+14*x^2)) \\ _G. C. Greubel_, Sep 09 2017
%Y A164072 Cf. A081179, A164031.
%K A164072 nonn
%O A164072 0,2
%A A164072 _Klaus Brockhaus_, Aug 09 2009