|
| |
|
|
A106256
|
|
Numbers n such that 12*n^2 + 13 is a square.
|
|
2
|
|
|
|
1, 3, 17, 43, 237, 599, 3301, 8343, 45977, 116203, 640377, 1618499, 8919301, 22542783, 124229837, 313980463, 1730298417, 4373183699, 24099948001, 60910591323, 335668973597, 848375094823, 4675265682357, 11816340736199
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
Recurrence: a(1)=1, a(2)=3, a(3)=14*a(1)+a(2), a(4)=14*a(2)+a(1) then a(n)=14*a(n-2)-a(n-4).
G.f.: x*(x+1)^3 / ((x^2-4*x+1)*(x^2+4*x+1)). - Corrected by Colin Barker, Apr 16 2014
|
|
|
EXAMPLE
|
12*1^2+13 = 5^2.
12*3^2+13 = 11^2.
12*17^2+13 = 59^2.
|
|
|
PROG
|
(PARI) Vec(x*(x+1)^3/((x^2-4*x+1)*(x^2+4*x+1)) + O(x^100)) \\ Colin Barker, Apr 16 2014
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
