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 A098305 #24 Mar 21 2024 06:49:09
%S A098305 0,1,5,36,245,1681,11520,78961,541205,3709476,25425125,174266401,
%T A098305 1194439680,8186811361,56113239845,384605867556,2636127833045,
%U A098305 18068288963761,123841894913280,848824975429201,5817932933091125,39876705556208676,273319005960369605,1873356336166378561
%N A098305 Unsigned member r=-5 of the family of Chebyshev sequences S_r(n) defined in A092184.
%C A098305 ((-1)^(n+1))*a(n) = S_{-5}(n), n>=0, defined in A092184.
%H A098305 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A098305 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,6,-1).
%F A098305 a(n) = 2*(T(n, 7/2)-(-1)^n)/9, with twice the Chebyshev polynomials of the first kind evaluated at x=7/2: 2*T(n, 7/2) = A056854(n) = ((7+sqrt(45))^n + (7-sqrt(45))^n)/2^n.
%F A098305 a(n) = 7*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
%F A098305 a(n) = 6*a(n-1) + 6*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=5.
%F A098305 G.f.: x*(1-x)/((1+x)*(1-7*x+x^2)) = x*(1-x)/(1-6*x-6*x^2+x^3) (from the Stephan link, see A092184).
%F A098305 a(n) = (Lucas(4*n) - 2*(-1)^n)/9. - _Greg Dresden_, Oct 10 2020
%Y A098305 Cf. A000032 (Lucas), A056854, A092184.
%K A098305 nonn,easy
%O A098305 0,3
%A A098305 _Wolfdieter Lang_, Oct 18 2004
%E A098305 More terms from _Michel Marcus_, Oct 11 2020