OFFSET
1,2
COMMENTS
The terms of the sequence are the squares of the y-values in the solution to the Pellian equation x^2-10*y^2=1. - Colin Barker, Sep 28 2013
After 0, the sequence lists the numbers k for which A055437(k) is a perfect square. - Bruno Berselli, Jan 16 2018
LINKS
Colin Barker, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (1443,-1443,1).
FORMULA
G.f.: 36*x^2*(1 + x) / ((1 - x)*(1 - 1442*x + x^2)). - Colin Barker, Jan 31 2013
a(0)=0, a(1)=36, a(2)=51984, a(n) = 1443*a(n-1)-1443*a(n-2)+a(n-3). - Harvey P. Dale, Dec 23 2013
a(n) = (721 + 228*sqrt(10))^(-n)*(721+228*sqrt(10) - 2*(721+228*sqrt(10))^n + (721-228*sqrt(10))*(721+228*sqrt(10))^(2*n)) / 40. - Colin Barker, Dec 29 2017
EXAMPLE
36 is a term because both 36 and 361 are squares.
MATHEMATICA
LinearRecurrence[{1443, -1443, 1}, {0, 36, 51984}, 20] (* Harvey P. Dale, Dec 23 2013 *)
PROG
(PARI) concat(0, Vec(36*x^2*(1 + x) / ((1 - x)*(1 - 1442*x + x^2)) + O(x^15))) \\ Colin Barker, Dec 29 2017
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved
