0,1

E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969), pps. 231-242.

A. F. Horadam, Special Properties of the Sequence W(n){a,b; p,q}, Fib. Quart., 5 (1967), pps. 424-434.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

Index entries for sequences related to Chebyshev polynomials.

a(n) = 7*S(n-1, 7) - 2*S(n-2, 7) = S(n, 7) - S(n-2, 7) = 2*T(n, 7/2), with S(n, x) := U(n, x/2), S(-1, x) := 0, S(-2, x) := -1. U(n, x), resp. T(n, x), are Chebyshev's polynomials of the second, resp. first, kind. S(n-1, 7) = A004187(n), n>=0. See A049310 and A053120.

a(n)=((7+sqrt(45))/2)^n + ((7-sqrt(45))/2)^n.

G.f.: (2-7x)/(1-7x+x^2).

a(n)=A005248(2*n). Bisection of A005248.

a[0] = 2; a[1] = 7; a[n_] := 7a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 19}] (from Robert G. Wilson v Jan 30 2004)

(PARI) a(n)=if(n<0, 0, polsym(1-7*x+x^2, n)[n+1])

(PARI) a(n)=if(n<0, 0, 2*subst(poltchebi(n), x, 7/2))

sage: [lucas_number2(n, 7, 1) for n in range(27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

a(n)=sqrt{[45*(A004187(n))^2]+4}.

a(n) = A000032(4n) = Lucas numbers L(4n).

Sequence in context: A054555 A072287 A091117 this_sequence A117141 A125813 A106159

Adjacent sequences: A056851 A056852 A056853 this_sequence A056855 A056856 A056857

easy,nonn

Barry E. Williams, Aug 29 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 31 2000

Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 31 2002