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A069128
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Centered 15-gonal numbers: a(n) = (15*n^2 - 15*n + 2)/2.
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6
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1, 16, 46, 91, 151, 226, 316, 421, 541, 676, 826, 991, 1171, 1366, 1576, 1801, 2041, 2296, 2566, 2851, 3151, 3466, 3796, 4141, 4501, 4876, 5266, 5671, 6091, 6526, 6976, 7441, 7921, 8416, 8926, 9451, 9991, 10546, 11116, 11701, 12301, 12916, 13546, 14191, 14851, 15526
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OFFSET
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1,2
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COMMENTS
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Centered pentadecagonal numbers or centered quindecagonal numbers or centered pentakaidecagonal numbers. - Omar E. Pol, Oct 03 2011
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LINKS
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FORMULA
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a(n) = (15*n^2 - 15*n + 2)/2.
G.f.: -x*(1+13*x+x^2) / (x-1)^3. - R. J. Mathar, Feb 04 2011
Binomial transform of [1, 15, 15, 0, 0, 0, ...] and Narayana transform (A001263) of [1, 15, 0, 0, 0, ...]. - Gary W. Adamson, Jul 28 2011
Sum_{n>=1} 1/a(n) = 2*Pi*tan(sqrt(7/15)*Pi/2)/sqrt(105).
Sum_{n>=1} a(n)/n! = 17*e/2 - 1.
Sum_{n>=1} (-1)^n * a(n)/n! = 17/(2*e) - 1. (End)
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EXAMPLE
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a(5) = 151 because (15*5^2 - 15*5 + 2)/2 = 151.
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 16, 46}, 50] (* Harvey P. Dale, Oct 22 2013 *)
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PROG
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(Magma) [(15*n^2 - 15*n + 2)/2 : n in [1..50]]; // Wesley Ivan Hurt, Nov 14 2014
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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