OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..500
F. T. Adams-Watters, SeqFan Discussion, Oct 2009
Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-1,1).
FORMULA
{k: 19+k*(k+1)/2 in A000290}.
a(n)= +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5).
G.f.: x*(3 +6*x +3*x^2 -6*x^3 -4*x^4)/((1-x) * (x^2-2*x-1) * (x^2+2*x-1)).
EXAMPLE
3*(3+1)/2+19 = 5^2. 9*(9+1)/2+19 = 8^2. 30*(30+1)/2+19 = 22^2. 60*(60+1)/2+19 = 43^2.
MATHEMATICA
Join[{3, 9}, Select[Range[0, 10^5], ( Ceiling[Sqrt[#*(# + 1)/2]] )^2 - #*(# + 1)/2 == 19 &]] (* or *) LinearRecurrence[{1, 6, -6, -1, 1}, {3, 9, 30, 60, 179}, 25] (* G. C. Greubel, Sep 03 2016 *)
PROG
(PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 19), print1(n, ", ") ) ); }
CROSSREFS
KEYWORD
nonn,less
AUTHOR
R. J. Mathar, Oct 18 2009
STATUS
approved