A195163 1000-gonal numbers: a(n) = n*(499*n - 498).

0, 1, 1000, 2997, 5992, 9985, 14976, 20965, 27952, 35937, 44920, 54901, 65880, 77857, 90832, 104805, 119776, 135745, 152712, 170677, 189640, 209601, 230560, 252517, 275472, 299425, 324376, 350325, 377272, 405217, 434160, 464101, 495040, 526977, 559912, 593845, 628776

Offset

0,3

Comments

a(A271470(n)) is a perfect square. In fact, a(A271470(n)) = A271105(n) if the first term of a(n) is 1. - Muniru A Asiru, Apr 10 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

M. A. Asiru, All square chiliagonal numbers, Int J Math Educ Sci Technol, 47:7(2016), 1123-1134.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 998*n*(n-1)/2 + n, according to the common formula for s-gonal numbers, a(n) = (s-2)*n*(n-1)/2 + n. - Sergey Pavlov, Aug 14 2015

G.f.: x*(1+997*x)/(1-x)^3. - R. J. Mathar, Sep 12 2011

E.g.f.: exp(x)*x*(1 + 499*x). - Ilya Gutkovskiy, Apr 10 2016

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 4. - Muniru A Asiru, Sep 12 2017

Maple

A195163:=n->n*(499*n - 498): seq(A195163(n), n=0..50); # Wesley Ivan Hurt, Sep 16 2017

Mathematica

LinearRecurrence[{3, -3, 1}, {0, 1, 1000}, 50] (* Vincenzo Librandi, Nov 25 2011 *)
PolygonalNumber[1000, Range[0, 40]] (* Harvey P. Dale, Sep 15 2022 *)

Prog

(PARI) a(n)=n*(499*n-498) \\ Charles R Greathouse IV, Sep 11 2011
(PARI) x='x+O('x^99); concat(0, Vec(x*(1+997*x)/(1-x)^3)) \\ Altug Alkan, Apr 10 2016
(Magma) [n*(499*n-498): n in [0..45]]; // Vincenzo Librandi, Nov 25 2011
(JavaScript) function a(n){return 998*n*(n-1)/2+n} // Sergey Pavlov, Aug 14 2015
(GAP)
a:=[0, 1, 1000];; for n in [4..10^2] do a[n]:=3*a[n-1]-3*a[n-2]+*a[n-3]; od; a;  # Muniru A Asiru, Sep 12 2017

Crossrefs

Cf. A000578, A092182.

Sequence in context: A168650 A043491 A100988 * A017175 A019548 A017271

Adjacent sequences: A195160 A195161 A195162 * A195164 A195165 A195166

Keyword

nonn,easy

Author

Kausthub Gudipati, Sep 10 2011

Status

approved