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A158536
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a(n) = 121*n^2 + 11.
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2
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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
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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FORMULA
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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)
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)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {11, 132, 495}, 50] (* Vincenzo Librandi, Feb 12 2012 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,less,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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