A030240 Scaled Chebyshev U-polynomials evaluated at sqrt(7)/2.
1, 7, 42, 245, 1421, 8232, 47677, 276115, 1599066, 9260657, 53631137, 310593360, 1798735561, 10416995407, 60327818922, 349375764605, 2023335619781, 11717718986232, 67860683565157, 393000752052475, 2275980479411226, 13180858091511257, 76334143284700217
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- A. F. Horadam, Special properties of the sequence W_n(a,b; p,q), Fib. Quart., 5.5 (1967), 424-434. Case n->n+1, a=0,b=1; p=7, q=-7.
- W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38 (2000) 408-419. Eqs. (38) and (45), lhs, m=7.
- Index entries for sequences related to Chebyshev polynomials.
- Index entries for linear recurrences with constant coefficients, signature (7,-7).
Programs
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Mathematica
Join[{a=1,b=7},Table[c=7*b-7*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 18 2011 *) -
PARI
Vec(1/(1-7*x+7*x^2) + O(x^30)) \\ Colin Barker, Jun 14 2015
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Sage
[lucas_number1(n,7,7) for n in range(1, 21)] # Zerinvary Lajos, Apr 23 2009
Formula
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)
a(n) = Sum_{k=0..n} A109466(n,k)*7^k. - Philippe Deléham, Oct 28 2008
Comments