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A154575
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a(n) = 2*n^2 + 12*n + 4.
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1
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18, 36, 58, 84, 114, 148, 186, 228, 274, 324, 378, 436, 498, 564, 634, 708, 786, 868, 954, 1044, 1138, 1236, 1338, 1444, 1554, 1668, 1786, 1908, 2034, 2164, 2298, 2436, 2578, 2724, 2874, 3028, 3186, 3348, 3514, 3684, 3858, 4036, 4218, 4404, 4594, 4788
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OFFSET
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1,1
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COMMENTS
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2*a(n) + 28 is a square.
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LINKS
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FORMULA
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G.f.: -2*x*(2*x-3)*(x-3) / (x-1)^3. (End)
Sum_{n>=1} 1/a(n) = 1/28 - cot(sqrt(7)*Pi)*Pi/(4*sqrt(7)).
Sum_{n>=1} (-1)^(n+1)/a(n) = 31/84 - cosec(sqrt(7)*Pi)*Pi/(4*sqrt(7)). (End)
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MATHEMATICA
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PROG
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(Magma) I:=[18, 36, 58]; [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 26 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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STATUS
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approved
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