This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A155144 #23 Dec 31 2023 10:22:48 %S A155144 1,8,80,792,7848,77760,770472,7634088,75641040,749476152,7426054728, %T A155144 73579777920,729052493832,7223690445768,71574686456400, %U A155144 709185392119512,7026840707183208,69624234893724480,689859680408169192 %N A155144 a(n) = 9*a(n-1) + 9*a(n-2), n>2; a(0)=1, a(1)=8, a(2)=80. %H A155144 G. C. Greubel, <a href="/A155144/b155144.txt">Table of n, a(n) for n = 0..998</a> %H A155144 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,9). %F A155144 G.f.: (1-x-x^2)/(1-9*x-9*x^2). %F A155144 From _G. C. Greubel_, Mar 24 2021: (Start) %F A155144 a(n) = (1/9)*[n=0] - 8*3^(n-2)*ChebyshevU(n, -3*i/2). %F A155144 a(n) = (1/9)*[n=0] + 8*3^(n-2)*Fibonacci(n+1, 3). (End) %p A155144 m:=30; S:=series( (1-x-x^2)/(1-9*x-9*x^2), x, m+1): %p A155144 seq(coeff(S, x, j), j=0..m); # _G. C. Greubel_, Mar 24 2021 %t A155144 Join[{1},LinearRecurrence[{9,9},{8,80},20]] (* or *) CoefficientList[ Series[ (1-x-x^2)/(1-9x-9x^2),{x,0,20}],x] (* _Harvey P. Dale_, Jun 19 2011 *) %o A155144 (Magma) [1] cat [n le 2 select 8*(9*n-8) else 9*(Self(n-1) + Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Mar 24 2021 %o A155144 (Sage) [1]+[-8*(3*i)^(n-2)*chebyshev_U(n, -3*i/2) for n in (1..30)] # _G. C. Greubel_, Mar 24 2021 %Y A155144 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), A155132 (m=8), this sequence (m=9), A155157 (m=10). %K A155144 nonn %O A155144 0,2 %A A155144 _Philippe Deléham_, Jan 21 2009