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A158543
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a(n) = 144*n^2 - 12.
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2
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132, 564, 1284, 2292, 3588, 5172, 7044, 9204, 11652, 14388, 17412, 20724, 24324, 28212, 32388, 36852, 41604, 46644, 51972, 57588, 63492, 69684, 76164, 82932, 89988, 97332, 104964, 112884, 121092, 129588, 138372, 147444, 156804, 166452, 176388, 186612, 197124
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OFFSET
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1,1
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COMMENTS
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The identity (24*n^2 - 1)^2 - (144*n^2 - 12)*(2*n)^2 = 1 can be written as A158544(n)^2 - a(n)*A005843(n)^2 = 1.
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LINKS
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FORMULA
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G.f.: -x*(132 + 168*x - 12*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(2*sqrt(3)))*Pi/(2*sqrt(3)))/24.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(2*sqrt(3)))*Pi/(2*sqrt(3)) - 1)/24. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {132, 564, 1284}, 50] (* Vincenzo Librandi, Feb 14 2012 *)
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PROG
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(Magma) I:=[132, 564, 1284]; [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 14 2012
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CROSSREFS
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KEYWORD
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nonn,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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