OFFSET
0,3
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..930
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 linear recurrences with constant coefficients, signature (13,-13,1).
FORMULA
a(n) = (T(n, 6)-1)/5 with Chebyshev's polynomials of the first kind evaluated at x=6: T(n, 6)=A023038(n)= ((6+sqrt(35))^n + (6-sqrt(35))^n)/2.
a(n) = 12*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
a(n) = 13*a(n-1) - 13*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=14.
G.f.: x*(1+x)/((1-x)*(1-12*x+x^2)) = x*(1+x)/(1-13*x+13*x^2-x^3) (from the Stephan link, see A092184).
MATHEMATICA
LinearRecurrence[{13, -13, 1}, {0, 1, 14}, 18] (* Michael De Vlieger, Feb 23 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 18 2004
STATUS
approved