OFFSET
1,1
LINKS
F. T. Adams-Watters, SeqFan Discussion, Oct 2009
FORMULA
{k: 21+k*(k+1)/2 in A000290}
Conjectures: (Start)
a(n)= +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5).
G.f.: x*(-5-2*x-3*x^2+2*x^3+6*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)).
G.f.: ( 12 + (12+25*x)/(x^2-2*x-1) + 1/(x-1) + (-1-10*x)/(x^2+2*x-1) )/2. (End)
EXAMPLE
5, 7, 40, and 50 are terms:
5* (5+1)/2 + 21 = 6^2,
7* (7+1)/2 + 21 = 7^2,
40*(40+1)/2 + 21 = 29^2,
50*(50+1)/2 + 21 = 36^2.
MATHEMATICA
Select[Range[68*10^6], IntegerQ[Sqrt[21+(#(#+1))/2]]&] (* Harvey P. Dale, Mar 07 2017 *)
PROG
(PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 21), print1(n, ", ") ) ); }
CROSSREFS
KEYWORD
nonn,less
AUTHOR
R. J. Mathar, Oct 18 2009
STATUS
approved