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A051865
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13-gonal (or tridecagonal) numbers: a(n) = n*(11*n - 9)/2.
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31
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0, 1, 13, 36, 70, 115, 171, 238, 316, 405, 505, 616, 738, 871, 1015, 1170, 1336, 1513, 1701, 1900, 2110, 2331, 2563, 2806, 3060, 3325, 3601, 3888, 4186, 4495, 4815, 5146, 5488, 5841, 6205, 6580, 6966, 7363, 7771, 8190, 8620, 9061, 9513
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OFFSET
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0,3
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COMMENTS
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Sequence found by reading the line from 0, in the direction 0, 13, ... and the parallel line from 1, in the direction 1, 36, ..., in the square spiral whose vertices are the generalized 13-gonal numbers A195313. - 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(11*a(n) + 56*n + 1) = a(11*a(n) + 56*n) + a(11*n+1). - Vladimir Shevelev, Jan 24 2014
Product_{n>=2} (1 - 1/a(n)) = 11/13. - Amiram Eldar, Jan 21 2021
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MATHEMATICA
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CoefficientList[Series[x (1 + 10 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)
LinearRecurrence[{3, -3, 1}, {0, 1, 13}, 50] (* Harvey P. Dale, Jul 12 2014 *)
Table[n*(11*n - 9)/2, {n, 0, 100}] (* Robert Price, Oct 11 2018 *)
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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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