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A152734
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5 times pentagonal numbers: 5*n*(3*n-1)/2.
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14
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0, 5, 25, 60, 110, 175, 255, 350, 460, 585, 725, 880, 1050, 1235, 1435, 1650, 1880, 2125, 2385, 2660, 2950, 3255, 3575, 3910, 4260, 4625, 5005, 5400, 5810, 6235, 6675, 7130, 7600, 8085, 8585, 9100, 9630, 10175, 10735, 11310, 11900, 12505, 13125, 13760, 14410
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OFFSET
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0,2
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COMMENTS
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a(n) can be represented as a figurate number using n concentric pentagons (see example). - Omar E. Pol, Aug 21 2011
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = (9*log(3) - sqrt(3)*Pi)/15.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*(sqrt(3)*Pi- 6*log(2))/15. (End)
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EXAMPLE
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Illustration of initial terms as concentric pentagons (in a precise representation the pentagons should be strictly concentric):
.
. o
. o o
. o o
. o o o o
. o o o o o o
. o o o o o o
. o o o o o o o o o
.o o o o o o o o o o o o
. o o o o o o o o o o o o
. o o o o o o
. o o o o o o
. o o o o o o o o o o o o
. o o
. o o
. o o o o o o o o
.
. 5 25 60
(End)
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MAPLE
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MATHEMATICA
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5*PolygonalNumber[5, Range[0, 50]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 13 2020 *)
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PROG
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CROSSREFS
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Cf. sequences of the form n*(d*n+10-d)/2 indexed in A140090.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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