OFFSET
1,1
COMMENTS
The corresponding values of y are in A082651.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,18,0,-1).
FORMULA
a(n) = ((-2-r)^n*(r-5) + (5+r)*(r-2)^n + (15+7*r)*(r+2)^n + (2-r)^n*(7*r-15)) / (4*r) where r=sqrt(5).
a(n) = 18*a(n-2) - a(n-4) for n>3.
G.f.: 4*x*(1 - x)*(1 + 5*x + x^2) / ((1 + 4*x - x^2)*(1 - 4*x - x^2)).
EXAMPLE
56 is in the sequence because 56^2 = 3136 = 5*25^2+11.
MATHEMATICA
LinearRecurrence[{0, 18, 0, -1}, {4, 16, 56, 284}, 30] (* Harvey P. Dale, May 28 2020 *)
PROG
(PARI) Vec(4*x*(1 - x)*(1 + 5*x + x^2) / ((1 + 4*x - x^2)*(1 - 4*x - x^2)) + O(x^30))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 14 2017
STATUS
approved