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A158536
a(n) = 121*n^2 + 11.
2
11, 132, 495, 1100, 1947, 3036, 4367, 5940, 7755, 9812, 12111, 14652, 17435, 20460, 23727, 27236, 30987, 34980, 39215, 43692, 48411, 53372, 58575, 64020, 69707, 75636, 81807, 88220, 94875, 101772, 108911, 116292, 123915, 131780, 139887, 148236, 156827, 165660
OFFSET
0,1
COMMENTS
The identity (22*n^2+1)^2-(121*n^2+11) * (2*n)^2 = 1 can be written as A158537(n)^2 -a(n) * A005843(n)^2 = 1.
FORMULA
From R. J. Mathar, Oct 16 2009: (Start)
a(n)= 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 11*(1+9*x+12*x^2)/(1-x)^3. (End)
From Amiram Eldar, Mar 06 2023: (Start)
Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(11))*Pi/sqrt(11) + 1)/22.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(11))*Pi/sqrt(11) + 1)/22. (End)
MATHEMATICA
121Range[0, 40]^2+11 (* Harvey P. Dale, Mar 04 2011 *)
LinearRecurrence[{3, -3, 1}, {11, 132, 495}, 50] (* Vincenzo Librandi, Feb 12 2012 *)
PROG
(Magma) I:=[11, 132, 495]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 12 2012
(PARI) for(n=1, 40, print1(121*n^2+11", ")); \\ Vincenzo Librandi, Feb 12 2012
CROSSREFS
Sequence in context: A068645 A097258 A044041 * A229252 A242163 A105280
KEYWORD
nonn,less,easy
AUTHOR
Vincenzo Librandi, Mar 21 2009
EXTENSIONS
a(0) added by R. J. Mathar, Oct 16 2009
STATUS
approved