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A152994
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Nine times hexagonal numbers: a(n) = 9*n*(2*n-1).
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3
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0, 9, 54, 135, 252, 405, 594, 819, 1080, 1377, 1710, 2079, 2484, 2925, 3402, 3915, 4464, 5049, 5670, 6327, 7020, 7749, 8514, 9315, 10152, 11025, 11934, 12879, 13860, 14877, 15930, 17019, 18144, 19305, 20502, 21735, 23004, 24309, 25650, 27027, 28440, 29889, 31374
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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 line from 0, in the direction 0, 9,..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. - Omar E. Pol, Sep 18 2011
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LINKS
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FORMULA
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a(n) = Sum_{i = 2..10} P(i,n), where P(i,m) = m*((i-2)*m-(i-4))/2. - Bruno Berselli, Jul 04 2018
G.f.: 9*x*(1+3*x)/(1-x)^3.
E.g.f.: 9*x*(1+2*x)*exp(x). (End)
Sum_{n>=1} 1/a(n) = 2*log(2)/9.
Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi - 2*log(2))/18. (End)
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [9*n*(2*n-1): n in [0..40]]; // G. C. Greubel, Sep 01 2019
(Sage) [9*n*(2*n-1) for n in (0..40)] # G. C. Greubel, Sep 01 2019
(GAP) List([0..40], n-> 9*n*(2*n-1)); # G. C. Greubel, Sep 01 2019
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CROSSREFS
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Similar sequences are listed in A316466.
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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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