A098302 Member r=17 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 17, 256, 3825, 57121, 852992, 12737761, 190213425, 2840463616, 42416740817, 633410648641, 9458742988800, 141247734183361, 2109257269761617, 31497611312240896, 470354912413851825, 7023826074895536481

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..852

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 (16,-16,1).

Formula

a(n) = 2*(T(n, 15/2)-1)/13 with twice the Chebyshev polynomials of the first kind evaluated at x=15/2: 2*T(n, 15/2)=A078365(n)= ((15+sqrt(221))^n +(15-sqrt(221))^n)/2^n.

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

a(n) = 16*a(n-1) - 16*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=17.

G.f.: x*(1+x)/((1-x)*(1-15*x+x^2)) = x*(1+x)/(1-16*x+16*x^2-x^3) (from the Stephan link, see A092184).

Mathematica

LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 18] &[17] (* Michael De Vlieger, Feb 23 2021 *)

Crossrefs

Sequence in context: A217453 A015675 A029462 * A090457 A342481 A355876

Adjacent sequences: A098299 A098300 A098301 * A098303 A098304 A098305

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 18 2004

Status

approved