A069128 Centered 15-gonal numbers: a(n) = (15*n^2 - 15*n + 2)/2.
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
Offset: 1
Examples
a(5) = 151 because (15*5^2 - 15*5 + 2)/2 = 151.
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- E. Weisstein, Centered Polygonal Numbers
- Index entries for sequences related to centered polygonal numbers
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
-
Magma
[(15*n^2 - 15*n + 2)/2 : n in [1..50]]; // Wesley Ivan Hurt, Nov 14 2014
-
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 *)
-
PARI
a(n)=15*n*(n-1)/2+1 \\ Charles R Greathouse IV, Nov 15 2014
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)
E.g.f.: exp(x)*(1 + 15*x^2/2) - 1. - Nikolaos Pantelidis, Feb 07 2023
Comments