A261343 50-gonal numbers: a(n) = 48*n*(n-1)/2 + n.

0, 1, 50, 147, 292, 485, 726, 1015, 1352, 1737, 2170, 2651, 3180, 3757, 4382, 5055, 5776, 6545, 7362, 8227, 9140, 10101, 11110, 12167, 13272, 14425, 15626, 16875, 18172, 19517, 20910, 22351, 23840, 25377, 26962, 28595, 30276, 32005, 33782, 35607, 37480

Offset: 0

Author

Sergey Pavlov, Aug 15 2015

Keywords

• nonn
• easy

Comments

According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 50).

96*a(n) + 23^2 is a square.

Links

• Kelvin Voskuijl, Table of n, a(n) for n = 0..10000
• Index to sequences related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001107, A051872, A254474.

Programs

JavaScript

function a(n){return 48*n*(n-1)/2+n}

Magma

[n*(24*n-23): n in [0..40]]; // Vincenzo Librandi, Aug 17 2015

Maple

A261343:=n->n*(24*n-23): seq(A261343(n), n=0..40); # Wesley Ivan Hurt, Aug 20 2015

Mathematica

PolygonalNumber[50,Range[0,40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 11 2019 *)

PARI

first(m)=vector(m,n,n--;n*(24*n-23)) \\ Anders Hellström, Aug 15 2015

Formula

a(n) = n*(24*n - 23).

G.f.: x*(1+47*x)/(1-x)^3. - Vincenzo Librandi, Aug 17 2015

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Aug 17 2015

E.g.f.: exp(x)*(x + 24*x^2). - Nikolaos Pantelidis, Feb 10 2023