OFFSET
0,2
COMMENTS
Solutions to X*(X+1)=30*Y^2 with Y=A077421. - R. J. Mathar, Mar 14 2023
LINKS
Colin Barker, Table of n, a(n) for n = 0..700
Index entries for linear recurrences with constant coefficients, signature (23,-23,1).
FORMULA
sqrt(a(n)+1) + sqrt(a(n)) = (sqrt(6) + sqrt(5))^n.
sqrt(a(n)+1) - sqrt(a(n)) = (sqrt(6) - sqrt(5))^n.
a(n) = 23*a(n-1) - 23*a(n-2) + a(n-3) for n > 2.
From Colin Barker, Dec 24 2018: (Start)
G.f.: 5*x*(1 + x) / ((1 - x)*(1 - 22*x + x^2)).
a(n) = ((11+2*sqrt(30))^(-n) * (-1+(11+2*sqrt(30))^n)^2) / 4.
(End)
2*a(n) = A077422(n)-1. - R. J. Mathar, Mar 16 2023
EXAMPLE
(sqrt(6) + sqrt(5))^2 = 11 + 2*sqrt(30) = sqrt(121) + sqrt(120). So a(2) = 120.
PROG
(PARI) concat(0, Vec(5*x*(1 + x) / ((1 - x)*(1 - 22*x + x^2)) + O(x^20))) \\ Colin Barker, Dec 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 24 2018
STATUS
approved