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 A241606 #21 Aug 12 2023 23:00:41
%S A241606 1,11,95,781,6336,51205,413351,3335651,26915305,217172736,1752296281,
%T A241606 14138673395,114079985111,920471087701,7426955448000,59925473898301,
%U A241606 483517428660911,3901330906652795,31478457514091281,253988526230055936
%N A241606 A linear divisibility sequence of the fourth order related to A003779.
%C A241606 A003779, which counts spanning trees in the graph P_5 x P_n, is a linear divisibility sequence of order 16. It factors into two fourth-order linear divisibility sequences; this sequence is one of the factors, the other is A143699.
%C A241606 The present sequence is the case P1 = 11, P2 = 23, Q = 1 of the 3 parameter family of 4th-order linear divisibility sequences found by Williams and Guy.
%H A241606 H. C. Williams and R. K. Guy, <a href="http://dx.doi.org/10.1142/S1793042111004587">Some fourth-order linear divisibility sequences</a>, Intl. J. Number Theory 7 (5) (2011) 1255-1277.
%H A241606 H. C. Williams and R. K. Guy, <a href="http://www.emis.de/journals/INTEGERS/papers/a17self/a17self.pdf">Some Monoapparitic Fourth Order Linear Divisibility Sequences</a> Integers, Volume 12A (2012) The John Selfridge Memorial Volume
%H A241606 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (11,-25,11,-1).
%F A241606 O.g.f. x*(1 - x^2)/(1 - 11*x + 25*x^2 - 11*x^3 + x^4).
%F A241606 a(n) = A003779(n)/A143699(n).
%F A241606 a(n) = ( T(n,alpha) - T(n,beta) )/(alpha - beta), n >= 1, where alpha = 1/4*(11 + sqrt(29)), beta = 1/4*(11 - sqrt(29)) and where T(n,x) denotes the Chebyshev polynomial of the first kind.
%F A241606 a(n)= U(n-1,1/4*(7 - sqrt(5)))*U(n-1,1/4*(7 + sqrt(5))), n >= 1, where U(n,x) denotes the Chebyshev polynomial of the second kind.
%F A241606 a(n) = the bottom left entry of the 2X2 matrix T(n,M), where M is the 2 X 2 matrix [0, -23/4; 1, 11/2].
%F A241606 See the remarks in A100047 for the general connection between Chebyshev polynomials of the first kind and 4th-order linear divisibility sequences.
%F A241606 a(n) = 11*a(n-1) - 25*a(n-2) + 11*a(n-3) - a(n-4). - _Vaclav Kotesovec_, Apr 28 2014
%t A241606 a[n_] := ChebyshevU[n-1, 1/4*(7-Sqrt[5])]*ChebyshevU[n-1, 1/4*(7+Sqrt[5])]; Table[a[n]//Round, {n, 1, 20}] (* _Jean-François Alcover_, Apr 28 2014, after _Peter Bala_ *)
%Y A241606 Cf. A003779, A100047, A143699.
%K A241606 nonn,easy
%O A241606 1,2
%A A241606 _Peter Bala_, Apr 26 2014