|
%I #15 Sep 08 2022 08:45:28
%S 1,1,99,295,10193,49001,1086723,6926543,119265217,910405105,
%T 13389536259,115088367703,1528961752529,14221495172249,
%U 176752280339811,1732989592387775,20610950377737217,209321891217088609,2417905969074687267,25140035386206969607
%N a(n) = ((1 + 7*sqrt(2))^n + (1 - 7*sqrt(2))^n)/2.
%H T. D. Noe, <a href="/A125820/b125820.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, 97).
%F From _Philippe Deléham_, Dec 12 2006: (Start)
%F a(n) = 2*a(n-1) + 97*a(n-2), with a(0)=a(1)=1.
%F G.f.: (1-x)/(1-2*x-97*x^2). (End)
%t Expand[Table[((1+7Sqrt[2])^n +(1-7Sqrt[2])^n)/2, {n,0,30}]] (* Artur Jasinski *)
%t LinearRecurrence[{2, 97}, {1, 1}, 30] (* _T. D. Noe_, Mar 28 2012 *)
%o (PARI) my(x='x+O('x^30)); Vec((1-x)/(1-2*x-97*x^2)) \\ _G. C. Greubel_, Aug 03 2019
%o (Magma) I:=[1,1]; [n le 2 select I[n] else 2*Self(n-1) +97*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Aug 03 2019
%o (Sage) ((1-x)/(1-2*x-97*x^2)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 03 2019
%o (GAP) a:=[1,1];; for n in [3..30] do a[n]:=2*a[n-1]+97*a[n-2]; od; a; # _G. C. Greubel_, Aug 03 2019
%Y Cf. A125819.
%K nonn
%O 1,3
%A _Artur Jasinski_, Dec 10 2006
|
