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 A069128 Centered 15-gonal numbers: a(n) = (15*n^2 - 15*n + 2)/2. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Centered pentadecagonal numbers or centered quindecagonal numbers or centered pentakaidecagonal numbers. - Omar E. Pol, Oct 03 2011 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 E. Weisstein, Centered Polygonal Numbers Index entries for linear recurrences with constant coefficients, signature (3,-3,1) FORMULA a(n) = (15*n^2 - 15*n + 2)/2. a(n) = 15*n+a(n-1)-15 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010 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 a(n) = A194715(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(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) EXAMPLE a(5) = 151 because (15*5^2 - 15*5 + 2)/2 = 151. MAPLE A069128:=n->(15*n^2 - 15*n + 2)/2: seq(A069128(n), n=1..50); # Wesley Ivan Hurt, Nov 14 2014 MATHEMATICA FoldList[#1 + #2 &, 1, 15 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *) LinearRecurrence[{3, -3, 1}, {1, 16, 46}, 50] (* Harvey P. Dale, Oct 22 2013 *) PROG (MAGMA) [(15*n^2 - 15*n + 2)/2 : n in [1..50]]; // Wesley Ivan Hurt, Nov 14 2014 (PARI) a(n)=15*n*(n-1)/2+1 \\ Charles R Greathouse IV, Nov 15 2014 CROSSREFS Cf. A005448, A001844, A005891, A003215, A069099. Sequence in context: A244343 A235772 A235555 * A099003 A124709 A244094 Adjacent sequences:  A069125 A069126 A069127 * A069129 A069130 A069131 KEYWORD nonn,easy,nice AUTHOR Terrel Trotter, Jr., Apr 07 2002 STATUS approved

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Last modified April 15 19:43 EDT 2021. Contains 342977 sequences. (Running on oeis4.)