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A166143
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a(n) = 3*n^2 + 3*n - 5.
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2
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1, 13, 31, 55, 85, 121, 163, 211, 265, 325, 391, 463, 541, 625, 715, 811, 913, 1021, 1135, 1255, 1381, 1513, 1651, 1795, 1945, 2101, 2263, 2431, 2605, 2785, 2971, 3163, 3361, 3565, 3775, 3991, 4213, 4441, 4675, 4915, 5161, 5413, 5671, 5935, 6205
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = a(n-1)+6*n, a(1)=1.
G.f.: (5 - 16*x + 5*x^2)/(-1 + x)^3.
E.g.f.: (-5 + 6*x + 3*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=0} 1/a(n) = Pi*tan(sqrt(23/3)*Pi/2)/sqrt(69). - Vaclav Kotesovec, Jul 06 2021
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 13, 31}, 50] (* G. C. Greubel, Apr 26 2016 *)
Table[3 n^2 + 3 n - 5, {n, 45}] (* or *)
Rest@ CoefficientList[Series[(5 - 16 x + 5 x^2)/(-1 + x)^3, {x, 0, 45}], x] (* Michael De Vlieger, Apr 27 2016 *)
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PROG
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(Magma) [-5+3*n^2+3*n: n in [1..50]].
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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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