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A195878
y-values in the solution to 7*x^2-6 = y^2.
3
1, 13, 29, 209, 463, 3331, 7379, 53087, 117601, 846061, 1874237, 13483889, 29870191, 214896163, 476048819, 3424854719, 7586910913, 54582779341, 120914525789, 869899614737, 1927045501711, 13863811056451, 30711813501587, 220951077288479, 489461970523681
OFFSET
1,2
COMMENTS
When are both t+1 and 7*t+1 perfect squares? This problem gives the equation 7*x^2-6 = y^2.
FORMULA
a(n+4) = 16*a(n+2)-a(n) with a(1)=1, a(2)=13, a(3)=29, a(4)=209.
From Bruno Berselli, Nov 03 2011: (Start)
G.f.: x*(1+x)*(1+12*x+x^2)/(1-16*x^2+x^4).
a(n) = ((-(-1)^n+t)*(8+3*t)^floor(n/2)-((-1)^n+t)*(8-3*t)^floor(n/2))/2 with t=sqrt(7).
a(n)^2 = 7*A161852(n)^2-6. (End)
MATHEMATICA
LinearRecurrence[{0, 16, 0, -1}, {1, 13, 29, 209}, 25] (* Bruno Berselli, Nov 11 2011 *)
PROG
(Maxima) makelist(expand(((-(-1)^n+sqrt(7))*(8+3*sqrt(7))^floor(n/2)-((-1)^n+sqrt(7))*(8-3*sqrt(7))^floor(n/2))/2), n, 1, 25); /* Bruno Berselli, Nov 03 2011 */
CROSSREFS
Sequence in context: A166272 A358744 A317897 * A013545 A120273 A104817
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, Oct 26 2011
EXTENSIONS
More terms from Bruno Berselli, Nov 02 2011
STATUS
approved