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A254474
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30-gonal numbers: a(n) = n*(14*n-13).
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14
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0, 1, 30, 87, 172, 285, 426, 595, 792, 1017, 1270, 1551, 1860, 2197, 2562, 2955, 3376, 3825, 4302, 4807, 5340, 5901, 6490, 7107, 7752, 8425, 9126, 9855, 10612, 11397, 12210, 13051, 13920, 14817, 15742, 16695, 17676, 18685, 19722, 20787, 21880
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OFFSET
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0,3
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COMMENTS
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See comments in A255184.
Also star 15-gonal numbers.
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REFERENCES
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E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6 (28th row of the table).
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LINKS
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Luciano Ancora, Table of n, a(n) for n = 0..1000
Luciano Ancora, Polygonal and Pyramidal numbers, Section 1.
Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: x*(-1 - 27*x)/(-1 + x)^3.
a(n) = A000217(n) + 27*A000217(n-1).
a(n) = A051867(n) + 15*A000217(n-1).
Product_{n>=2} (1 - 1/a(n)) = 14/15. - Amiram Eldar, Jan 22 2021
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MATHEMATICA
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Table[n (14 n - 13), {n, 40}]
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PROG
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(PARI) a(n)=n*(14*n-13) \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Cf. similar sequences listed in A255184.
Sequence in context: A130862 A070756 A058903 * A103906 A124799 A126384
Adjacent sequences: A254471 A254472 A254473 * A254475 A254476 A254477
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KEYWORD
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nonn,easy
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AUTHOR
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Luciano Ancora, Apr 04 2015
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STATUS
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approved
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