A098300 Member r=15 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 15, 196, 2535, 32761, 423360, 5470921, 70698615, 913611076, 11806245375, 152567578801, 1971572279040, 25477872048721, 329240764354335, 4254652064557636, 54981236074894935, 710501416909076521

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..900

S. Barbero, U. Cerruti, and N. Murru, On polynomial solutions of the Diophantine equation (x + y - 1)^2 = wxy, Rendiconti Sem. Mat. Univ. Pol. Torino (2020) Vol. 78, No. 1, 5-12.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (14,-14,1).

Formula

a(n) = 2*(T(n, 13/2)-1)/11 with twice the Chebyshev polynomials of the first kind evaluated at x=13/2: 2*T(n, 13/2)=A078363(n)=((13+sqrt(165))^n + (13-sqrt(165))^n)/2^n.

a(n) = 13*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.

a(n) = 14*a(n-1) - 14*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=15.

G.f.: x*(1+x)/((1-x)*(1-13*x+x^2)) = x*(1+x)/(1-14*x+14*x^2-x^3) (from the Stephan link, see A092184).

Mathematica

LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 18] &[15] (* Michael De Vlieger, Feb 23 2021 *)

Crossrefs

Sequence in context: A172204 A015673 A125472 * A185899 A345445 A152587

Adjacent sequences: A098297 A098298 A098299 * A098301 A098302 A098303

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 18 2004

Status

approved