cp's OEIS Frontend

A030240 Scaled Chebyshev U-polynomials evaluated at sqrt(7)/2.

%I A030240 #30 Jan 05 2025 19:51:35
%S A030240 1,7,42,245,1421,8232,47677,276115,1599066,9260657,53631137,310593360,
%T A030240 1798735561,10416995407,60327818922,349375764605,2023335619781,
%U A030240 11717718986232,67860683565157,393000752052475,2275980479411226,13180858091511257,76334143284700217
%N A030240 Scaled Chebyshev U-polynomials evaluated at sqrt(7)/2.
%C A030240 Binomial transform of A030221. - _Philippe Deléham_, Nov 19 2009
%H A030240 Colin Barker, <a href="/A030240/b030240.txt">Table of n, a(n) for n = 0..1000</a>
%H A030240 A. F. Horadam, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/5-5/horadam.pdf">Special properties of the sequence W_n(a,b; p,q)</a>, Fib. Quart., 5.5 (1967), 424-434. Case n->n+1, a=0,b=1; p=7, q=-7.
%H A030240 W. Lang, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/38-5/lang.pdf">On polynomials related to powers of the generating function of Catalan's numbers</a>, Fib. Quart. 38 (2000) 408-419. Eqs. (38) and (45), lhs, m=7.
%H A030240 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A030240 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7).
%F A030240 a(n) = 7*a(n-1)-7*a(n-2), a(-1)=0, a(0)=1; a(n)=sqrt(7)^n*U(n, sqrt(7)/2); G.f.: 1/(1-7*x+7*x^2); a(2*k)=7^k*A030221(k); a(2*k-1)=7^k*A004254(k)
%F A030240 a(n) = Sum_{k=0..n} A109466(n,k)*7^k. - _Philippe Deléham_, Oct 28 2008
%t A030240 Join[{a=1,b=7},Table[c=7*b-7*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 18 2011 *)
%o A030240 (Sage) [lucas_number1(n,7,7) for n in range(1, 21)] # _Zerinvary Lajos_, Apr 23 2009
%o A030240 (PARI) Vec(1/(1-7*x+7*x^2) + O(x^30)) \\ _Colin Barker_, Jun 14 2015
%K A030240 nonn,easy
%O A030240 0,2
%A A030240 _Wolfdieter Lang_