A155132 - OEIS

%I #15 Dec 31 2023 10:22:44

%S 1,7,63,560,4984,44352,394688,3512320,31256064,278147072,2475225088,

%T 22026977280,196017618944,1744356769792,15522995109888,

%U 138138815037440,1229294481178624,10939466369728512,97350086807257088

%N a(n) = 8*a(n-1) + 8*a(n-2), n > 2, a(0)=1, a(1)=7, a(2)=63.

%H G. C. Greubel, <a href="/A155132/b155132.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 (8,8).

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

%F a(n) = (1/8)*[n=0] - 7*(2*sqrt(2)*i)^(n-2)*ChebyshevU(n, -sqrt(2)*I). - _G. C. Greubel_, Mar 24 2021

%t With[{m=8}, LinearRecurrence[{m, m}, {1, m-1, m^2-1}, 30]] (* _G. C. Greubel_, Mar 24 2021 *)

%o (Magma) [1] cat [n le 2 select 7*(8*n-7) else 8*(Self(n-1) + Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Mar 24 2021

%o (Sage) [1]+[-7*(2*sqrt(2)*i)^(n-2)*chebyshev_U(n, -sqrt(2)*i) for n in (1..30)] # _G. C. Greubel_, Mar 24 2021

%Y Sequences of the form a(n) = m*(a(n-1) + a(n-2)) with a(0)=1, a(1) = m-1, a(2) = m^2 -1: A155020 (m=2), A155116 (m=3), A155117 (m=4), A155119 (m=5), A155127 (m=6), A155130 (m=7), this sequence (m=8), A155144 (m=9), A155157 (m=10).

%K nonn

%O 0,2

%A _Philippe Deléham_, Jan 20 2009