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A069125
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a(n) = (11*n^2 - 11*n + 2)/2.
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13
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1, 12, 34, 67, 111, 166, 232, 309, 397, 496, 606, 727, 859, 1002, 1156, 1321, 1497, 1684, 1882, 2091, 2311, 2542, 2784, 3037, 3301, 3576, 3862, 4159, 4467, 4786, 5116, 5457, 5809, 6172, 6546, 6931, 7327, 7734, 8152, 8581, 9021, 9472, 9934, 10407, 10891
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OFFSET
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1,2
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COMMENTS
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Centered hendecagonal (11-gonal) numbers. - Omar E. Pol, Oct 03 2011
Numbers of the form (2*m+1)^2 + k*m*(m+1)/2: in this case is k=3. See also A254963. - Bruno Berselli, Feb 11 2015
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
X. Acloque, Polynexus Numbers and other mathematical wonders [broken link]
Eric Weisstein's World of Mathematics, Centered Polygonal Numbers
Index entries for sequences related to centered polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 1+ sum_{j=0..n-1} (11*j). - Xavier Acloque, Oct 22 2003
Binomial transform of [1, 11, 11, 0, 0, 0,...]; Narayana transform (A001263) of [1, 11, 0, 0, 0,...]. - Gary W. Adamson, Dec 29 2007
a(n) = 11*n+a(n-1)-11 with n>1, a(1)=1. - Vincenzo Librandi, Aug 08 2010
G.f. -x*(1+9*x+x^2) / (x-1)^3. - R. J. Mathar, Jun 05 2011
a(0)=1, a(1)=12, a(2)=34, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jun 25 2011
a(n) = A152740(n-1) + 1. - Omar E. Pol, Oct 03 2011
From Amiram Eldar, Jun 21 2020: (Start)
Sum_{n>=1} 1/a(n) = 2*Pi*tan(sqrt(3/11)*Pi/2)/sqrt(33).
Sum_{n>=1} a(n)/n! = 13*e/2 - 1.
Sum_{n>=1} (-1)^n * a(n)/n! = 13/(2*e) - 1. (End)
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EXAMPLE
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a(5)=111 because 111 = (11*5^2 - 11*5 + 2)/2 = (275 - 55 + 2)/2 = 222/2.
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MATHEMATICA
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FoldList[#1 + #2 &, 1, 11 Range@ 45] (* Robert G. Wilson v *)
Table[(11n^2-11n+2)/2, {n, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 12, 34}, 60] (* Harvey P. Dale, Jun 25 2011 *)
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PROG
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(PARI) a(n)=(11*n^2-11*n+2)/2 \\ Charles R Greathouse IV, Sep 24 2015
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CROSSREFS
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Cf. A001263, A001844, A003215, A005448, A005891, A069099.
Sequence in context: A098080 A068517 A113748 * A142245 A139635 A124705
Adjacent sequences: A069122 A069123 A069124 * A069126 A069127 A069128
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Terrel Trotter, Jr., Apr 07 2002
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EXTENSIONS
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More terms from Harvey P. Dale, Jun 25 2011
Name rewritten by Bruno Berselli, Feb 11 2015
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STATUS
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approved
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