OFFSET
1,3
COMMENTS
8 of the first 10 terms are of the form x^y. The two exceptions are a(7) = 311904 = 2^5 * 3^3 * 19^2 and a(10) = 449765784 = 2^3 * 3^5 * 13^2 * 37^2.
The corresponding squares are given by A075873(2*n-1)^2. E.g., triangular(a(10)) + triangular(2*a(10)) = 711142146^2 = A075873(19)^2.
Locations of squares in A147875, equivalent to solving the Diophantine equation n*(5*n+3)=2*s^2. - R. J. Mathar, Apr 19 2013
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1442,-1442,0,-1,1).
FORMULA
a(n) = (A228209(2*n-1) - 3) / 10. - Max Alekseyev, Sep 04 2013
G.f.: x^2*(x+1)*(x^4 + 23*x^3 + 168*x^2 + 23*x + 1) / (x^6 - 1442*x^3 + 1) / (1-x). - Max Alekseyev, Sep 04 2013
MATHEMATICA
LinearRecurrence[{1, 0, 1442, -1442, 0, -1, 1}, {0, 1, 25, 216, 1849, 36481, 311904}, 30] (* Harvey P. Dale, Jan 23 2015 *)
PROG
(Python)
import math
for i in range(1L<<30):
s = i*(i+1)/2 + i*(2*i+1)
t = int(math.sqrt(s))
if s == t*t: print i,
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Apr 18 2013
EXTENSIONS
Terms a(11) onward from Max Alekseyev, Sep 04 2013
STATUS
approved