A069130 Centered 17-gonal numbers: (17*n^2 - 17*n + 2)/2.

1, 18, 52, 103, 171, 256, 358, 477, 613, 766, 936, 1123, 1327, 1548, 1786, 2041, 2313, 2602, 2908, 3231, 3571, 3928, 4302, 4693, 5101, 5526, 5968, 6427, 6903, 7396, 7906, 8433, 8977, 9538, 10116, 10711, 11323, 11952, 12598, 13261, 13941, 14638, 15352

Offset

1,2

Comments

Equals binomial transform of [1, 17, 17, 0, 0, 0, ...]. - Gary W. Adamson, Mar 26 2010

Links

Ivan Panchenko, Table of n, a(n) for n = 1..1000

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)

Formula

a(n) = (17*n^2 - 17*n + 2)/2.

a(n) = 17*n + a(n-1) - 17 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010

G.f.: x*(1+15*x+x^2) / (1-x)^3. - R. J. Mathar, Feb 04 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=18, a(2)=52. - Harvey P. Dale, Jun 05 2011

Narayana transform (A001263) of [1, 17, 0, 0, 0, ...]. - Gary W. Adamson, Jul 28 2011

From Amiram Eldar, Jun 21 2020: (Start)

Sum_{n>=1} 1/a(n) = 2*Pi*tan(3*Pi/(2*sqrt(17)))/(3*sqrt(17)).

Sum_{n>=1} a(n)/n! = 19*e/2 - 1.

Sum_{n>=1} (-1)^n * a(n)/n! = 19/(2*e) - 1. (End)

E.g.f.: exp(x)*(1 + 17*x^2/2) - 1. - Stefano Spezia, May 31 2022

Example

a(5) = 171 because (17*5^2 - 17*5 + 2)/2 = (425 - 85 + 2)/2 = 342/2 = 171.

Maple

A069130:=n->(17*n^2 - 17*n + 2)/2; seq(A069130(n), n=1..50); # Wesley Ivan Hurt, Jun 09 2014

Mathematica

FoldList[#1 + #2 &, 1, 17 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)
Table[(17n^2-17n+2)/2, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 18, 52}, 50] (* Harvey P. Dale, Jun 05 2011 *)

Prog

(PARI) a(n)=17*binomial(n, 2)+1 \\ Charles R Greathouse IV, Jun 05 2011
(Magma) [ (17*n^2 - 17*n + 2)/2 : n in [1..50] ]; // Wesley Ivan Hurt, Jun 09 2014

Crossrefs

Cf. centered polygonal numbers listed in A069190.

Sequence in context: A051870 A262454 A175815 * A299071 A124711 A126372

Adjacent sequences: A069127 A069128 A069129 * A069131 A069132 A069133

Keyword

easy,nice,nonn

Author

Terrel Trotter, Jr., Apr 07 2002

Extensions

Typo in formula fixed by Omar E. Pol, Dec 22 2008

Status

approved