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A051872
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20-gonal (or icosagonal) numbers: a(n) = n*(9*n-8).
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13
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0, 1, 20, 57, 112, 185, 276, 385, 512, 657, 820, 1001, 1200, 1417, 1652, 1905, 2176, 2465, 2772, 3097, 3440, 3801, 4180, 4577, 4992, 5425, 5876, 6345, 6832, 7337, 7860, 8401, 8960, 9537, 10132, 10745, 11376, 12025, 12692, 13377, 14080
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OFFSET
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0,3
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COMMENTS
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This sequence does not contain any squares other than 0 and 1. See A188896. - T. D. Noe, Apr 13 2011
Sequence found by reading the line from 0, in the direction 0, 20,... and the parallel line from 1, in the direction 1, 57,..., in the square spiral whose vertices are the generalized 20-gonal numbers. - Omar E. Pol, Jul 18 2012
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REFERENCES
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Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
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LINKS
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FORMULA
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a(18*a(n) + 154*n + 1) = a(18*a(n) + 154*n) + a(18*n + 1). - Vladimir Shevelev, Jan 24 2014
Product_{n>=2} (1 - 1/a(n)) = 9/10. - Amiram Eldar, Jan 22 2021
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MAPLE
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MATHEMATICA
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PolygonalNumber[20, Range[0, 50]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 14 2017 *)
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PROG
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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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