A167149 10000-gonal numbers: a(n) = n + 4999 * n * (n-1).

0, 1, 10000, 29997, 59992, 99985, 149976, 209965, 279952, 359937, 449920, 549901, 659880, 779857, 909832, 1049805, 1199776, 1359745, 1529712, 1709677, 1899640, 2099601, 2309560, 2529517, 2759472, 2999425, 3249376, 3509325, 3779272, 4059217, 4349160, 4649101

Offset: 0

Author

Michael G. Fenner (sidk.20c(AT)gmail.com), Oct 28 2009

Keywords

• nonn
• easy

Comments

There are infinitely many 10000-gonal numbers that are also squares. The first seven are at n = 0, 1, 2, 21, 9800, 173774514938177, 1042188013912456. - Muniru A Asiru, Apr 10 2016

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A057145. - R. J. Mathar, Nov 02 2009

Programs

GAP

A167149:=List([1..10^2],n->n+499*n*(n-1)); # Muniru A Asiru, Sep 27 2017

Maple

P := proc(n,k) n*((k-2)*n-k+4)/2 ; end: A167149 := proc(n) P(n,10000) ; end: seq(A167149(n),n=0..50) ; # R. J. Mathar, Nov 02 2009

Mathematica

Table[n + 4999 n (n - 1), {n, 0, 31}] (* or *)
CoefficientList[Series[x (1 + 9997 x)/(1 - x)^3, {x, 0, 31}], x] (* Michael De Vlieger, Apr 10 2016 *)
LinearRecurrence[{3, -3, 1}, {0, 1, 10000}, 10] (* G. C. Greubel, Jun 04 2016 *)

PARI

x='x+O('x^99); concat(0, Vec(x*(1+9997*x)/(1-x)^3)) \\ Altug Alkan, Apr 10 2016

Formula

From R. J. Mathar, Nov 02 2009: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(1 + 9997*x)/(1-x)^3. (End)

E.g.f.: exp(x)*x*(1 + 4999*x). - Ilya Gutkovskiy, Apr 10 2016

Extensions

Edited (but not checked) by N. J. A. Sloane, Nov 01 2009

Sequence extended by R. J. Mathar, Nov 02 2009