A098305 Unsigned member r=-5 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 5, 36, 245, 1681, 11520, 78961, 541205, 3709476, 25425125, 174266401, 1194439680, 8186811361, 56113239845, 384605867556, 2636127833045, 18068288963761, 123841894913280, 848824975429201, 5817932933091125, 39876705556208676, 273319005960369605, 1873356336166378561

Offset: 0

Author

Wolfdieter Lang, Oct 18 2004

Keywords

• nonn
• easy

Comments

((-1)^(n+1))*a(n) = S_{-5}(n), n>=0, defined in A092184.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (6,6,-1).

Crossrefs

Cf. A000032 (Lucas), A056854, A092184.

Formula

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.

a(n) = 7*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.

a(n) = 6*a(n-1) + 6*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=5.

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).

a(n) = (Lucas(4*n) - 2*(-1)^n)/9. - Greg Dresden, Oct 10 2020

Extensions

More terms from Michel Marcus, Oct 11 2020