A098304 Member r=19 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 19, 324, 5491, 93025, 1575936, 26697889, 452288179, 7662201156, 129805131475, 2199025033921, 37253620445184, 631112522534209, 10691659262636371, 181127094942284100, 3068468954756193331

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..814

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 (18,-18,1).

Formula

a(n) = 2*(T(n, 17/2)-1)/15 with twice the Chebyshev polynomials of the first kind evaluated at x=17/2: 2*T(n, 17/2) = A078367(n) = ((17+sqrt(285))^n + (17-sqrt(285))^n)/2^n.

a(n) = 17*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.

a(n) = 18*a(n-1) - 18*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=19.

G.f.: x*(1+x)/((1-x)*(1-17*x+x^2)) = x*(1+x)/(1-18*x+18*x^2-x^3) (from the Stephan link, see A092184).

Mathematica

LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 17] &[19] (* Michael De Vlieger, Feb 23 2021 *)

Crossrefs

Sequence in context: A027541 A143699 A015676 * A014900 A121324 A093973

Adjacent sequences: A098301 A098302 A098303 * A098305 A098306 A098307

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 18 2004

Status

approved