A164072 - OEIS

%I #10 Sep 08 2022 08:45:47

%S 1,7,42,238,1316,7196,39144,212408,1151248,6236272,33772704,182873824,

%T 990172736,5361148352,29026768512,157158071168,850889810176,

%U 4606905485056,24942786537984,135045615513088,731165912572928

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

%C Binomial transform of A081179 without initial 0. Inverse binomial transform of A164031.

%H G. C. Greubel, <a href="/A164072/b164072.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-14).

%F a(n) = ((2+3*sqrt(2))*(4+sqrt(2))^n + (2-3*sqrt(2))*(4-sqrt(2))^n)/4.

%F G.f.: (1-x)/(1-8*x+14*x^2).

%F 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 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 (Magma) [ n le 2 select 6*n-5 else 8*Self(n-1)-14*Self(n-2): n in [1..21] ];

%o (PARI) x='x+O('x^50); Vec((1-x)/(1-8*x+14*x^2)) \\ _G. C. Greubel_, Sep 09 2017

%Y Cf. A081179, A164031.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Aug 09 2009