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 A069125 a(n) = (11*n^2 - 11*n + 2)/2. 13
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS 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 linear recurrences with constant coefficients, signature (3,-3,1). FORMULA 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) EXAMPLE a(5)=111 because 111 = (11*5^2 - 11*5 + 2)/2 = (275 - 55 + 2)/2 = 222/2. MATHEMATICA 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 *) PROG (PARI) a(n)=(11*n^2-11*n+2)/2 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A001263, A001844, A003215, A005448, A005891, A069099. Sequence in context: A098080 A068517 A113748 * A142245 A139635 A124705 Adjacent sequences:  A069122 A069123 A069124 * A069126 A069127 A069128 KEYWORD nonn,easy,nice AUTHOR Terrel Trotter, Jr., Apr 07 2002 EXTENSIONS More terms from Harvey P. Dale, Jun 25 2011 Name rewritten by Bruno Berselli, Feb 11 2015 STATUS approved

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Last modified September 19 01:52 EDT 2020. Contains 337175 sequences. (Running on oeis4.)