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

0,3

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).

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

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 *)

Prog

(PARI) x='x+O('x^99); concat(0, Vec(x*(1+9997*x)/(1-x)^3)) \\ Altug Alkan, Apr 10 2016
(GAP)
A167149:=List([1..10^2], n->n+499*n*(n-1)); # Muniru A Asiru, Sep 27 2017

Crossrefs

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

Sequence in context: A004270 A168651 A043492 * A277398 A326640 A017176

Adjacent sequences: A167146 A167147 A167148 * A167150 A167151 A167152

Keyword

nonn,easy

Author

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

Extensions

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

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

Status

approved