OFFSET
1,2
COMMENTS
From Lamine Ngom, Oct 27 2020: (Start)
Also numbers k such that 1+64*k is a square. (End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
G.f.: x^2*(15+2*x+15*x^2)/((1+x)^2*(1-x)^3 ). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009; checked and corrected by R. J. Mathar, Sep 16 2009]
a(n) = (2*n-1 + 7/8*(-1)^n)^2 -1/64. - Robert Israel, Apr 20 2014
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). - Wesley Ivan Hurt, Nov 10 2020
Sum_{n>=2} 1/a(n) = 16 - (sqrt(2*(2+sqrt(2))) + sqrt(2) + 1)*Pi. - Amiram Eldar, Mar 17 2022
EXAMPLE
MAPLE
seq((2*n-1 + 7/8*(-1)^n)^2 - 1/64, n = 1 .. 1000); # Robert Israel, Apr 20 2014
MATHEMATICA
Array[(2 # - 1 + 7/8*(-1)^#)^2 - 1/64 &, 46] (* or *)
Rest@ CoefficientList[Series[x^2*(15 + 2 x + 15 x^2)/((1 + x)^2*(1 - x)^3), {x, 0, 46}], x] (* Michael De Vlieger, Nov 05 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Mar 04 2009
EXTENSIONS
Definition edited by N. J. A. Sloane, Mar 08 2009
STATUS
approved