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A033568
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Second pentagonal numbers with odd index: a(n) = (2*n-1)*(3*n-1).
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15
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1, 2, 15, 40, 77, 126, 187, 260, 345, 442, 551, 672, 805, 950, 1107, 1276, 1457, 1650, 1855, 2072, 2301, 2542, 2795, 3060, 3337, 3626, 3927, 4240, 4565, 4902, 5251, 5612, 5985, 6370, 6767, 7176, 7597, 8030, 8475, 8932, 9401, 9882, 10375, 10880, 11397, 11926
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OFFSET
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0,2
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COMMENTS
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Sequence found by reading the segment (1, 2) together with the line (one of the diagonal axes) from 2, in the direction 2, 15, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011
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LINKS
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FORMULA
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G.f.: (1-x+12*x^2)/(1-x)^3.
Sum_{n>=0} 1/a(n) = 1 + Pi/(2*sqrt(3)) + 2*log(2) - 3*log(3)/2.
Sum_{n>=0} (-1)^n/a(n) = 1 + (1/sqrt(3) - 1/2)*Pi - log(2). (End)
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 2, 15}, 50] (* Ray Chandler, Dec 08 2011 *)
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PROG
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(Magma) [(2*n-1)*(3*n-1): n in [0..50]]; // G. C. Greubel, Oct 12 2019
(Sage) [(2*n-1)*(3*n-1) for n in range(50)] # G. C. Greubel, Oct 12 2019
(GAP) List([0..50], n-> (2*n-1)*(3*n-1)); # G. C. Greubel, Oct 12 2019
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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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