This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A069129 Centered 16-gonal numbers. 32
 1, 17, 49, 97, 161, 241, 337, 449, 577, 721, 881, 1057, 1249, 1457, 1681, 1921, 2177, 2449, 2737, 3041, 3361, 3697, 4049, 4417, 4801, 5201, 5617, 6049, 6497, 6961, 7441, 7937, 8449, 8977, 9521, 10081, 10657, 11249, 11857, 12481, 13121, 13777, 14449 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, sequence found by reading the line from 1, in the direction 1, 17,..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A139098 in the same spiral. - Omar E. Pol, Apr 26 2008 The subsequence of primes begins: 17, 97, 241, 337, 449, 577, 881, 1249, 3041, 3361, 3697, 4049, 4801, 6961, 7937, 9521,  10657, 13121, 14449. See A184899: n such that the n-th centered 12-gonal number is prime. Indices of prime star numbers. - Jonathan Vos Post, Feb 27, 2011 Binomial transform of [1, 16, 16, 0, 0, 0,...] and Narayana transform (A001263) of [1, 16, 0, 0, 0,...]. - Gary W. Adamson, Jul 28 2011 Centered hexadecagonal numbers or centered hexakaidecagonal numbers. - Omar E. Pol, Oct 03 2011 a(n) = m(n,n) for an array constructed by using the terms in A016813 as the antidiagonals; the first few antidiagonals are 1; 5,9; 13,17,21; 25,29,33,37. - J. M. Bergot, Jul 05 2013 [The first five rows begin: 1,9,21,37,57; 5,17,33,53,77; 13,29,49,73,101; 25,45,69,97,129; 41,65,93,125,161.] LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Centered Polygonal Numbers Index entries for linear recurrences with constant coefficients, signature (3,-3,1) FORMULA a(n) = 8*n^2 - 8*n + 1. a(n) = A035008(n-1) + 1. - Omar E. Pol, Apr 26 2008 a(n) = 16*n + a(n-1) - 16 with n>1, a(1)=1. - Vincenzo Librandi, Aug 08 2010 G.f.: -x*(1+14*x+x^2) / (x-1)^3. - R. J. Mathar, Feb 04 2011 E.g.f.: (8*x^2 + 1)*exp(x). - G. C. Greubel, Jul 18 2017 a(n) = A056220(2n-1). - Bruce J. Nicholson, Aug 31 2017 EXAMPLE a(5) = 161 because 8*5^2 - 8*5 + 1 = 200 - 40 + 1 = 161. MATHEMATICA FoldList[#1 + #2 &, 1, 16 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *) Rest[CoefficientList[Series[-x(1+14x+x^2)/(x-1)^3, {x, 0, 50}], x]]  (* Harvey P. Dale, Apr 22 2011 *) PROG (MAGMA) [8*n^2-8*n+1: n in [0..50]]; // Vincenzo Librandi, Feb 05 2013 (PARI) a(n)=8*n^2-8*n+1 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A005448, A001844, A005891, A003215, A069099, A000217, A035008, A139098. Bisection of A077221. Sequence in context: A239130 A181426 A029487 * A176273 A124710 A113867 Adjacent sequences:  A069126 A069127 A069128 * A069130 A069131 A069132 KEYWORD easy,nice,nonn AUTHOR Terrel Trotter, Jr., Apr 07 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)