OFFSET
0,2
COMMENTS
Also, numbers n such that 5*A000217(n) is a square. [Bruno Berselli, Dec 16 2013]
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..500
Kenneth M. Wilke, Problem 269, Crux Mathematicorum, Vol. 3, No. 7 (1977), p. 190; Solution to Problem 269 by Lindsay Reynolds, W. J. Blundon and M. S. Klamkin, ibid., Vol. 4, No. 3 (1978), pp. 79-82; Comment by the MaScoT Problems Group, ibid., Vol. 6, No. 2 (1980), pp. 44-46.
Index entries for linear recurrences with constant coefficients, signature (39,-39,1).
FORMULA
a(0)=0, a(1)=9 and a(n) = 38*a(n-1) - a(n-2) + 18.
a(n) = (A078986(n) - 1)/2. - Max Alekseyev, Nov 13 2009
G.f.: -9*x*(x+1)/((x-1)*(x^2-38*x+1)). - Colin Barker, Oct 24 2012
From Amiram Eldar, Feb 15 2022: (Start)
sqrt(a(n)+1) - sqrt(n) = (sqrt(10)-3)^n (Wilke, 1977).
a(n) = ((Sum_{k=0..n} binomial(2*n, 2*k) * 10^(n-k) * 9*k)- 1)/2 (Klamkin, 1978).
a(n) = sinh(n*log(sqrt(10)+3))^2 (MaScoT Problems Group, 1980). (End)
MATHEMATICA
LinearRecurrence[{39, -39, 1}, {0, 9, 360}, 30] (* Harvey P. Dale, Jun 01 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, Nov 14 2007
EXTENSIONS
More terms from Max Alekseyev, Nov 13 2009
STATUS
approved