OFFSET
0,3
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
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
MAPLE
MATHEMATICA
PolygonalNumber[50, Range[0, 40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 11 2019 *)
PROG
(JavaScript) function a(n){return 48*n*(n-1)/2+n}
(PARI) first(m)=vector(m, n, n--; n*(24*n-23)) \\ Anders Hellström, Aug 15 2015
(Magma) [n*(24*n-23): n in [0..40]]; // Vincenzo Librandi, Aug 17 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sergey Pavlov, Aug 15 2015
STATUS
approved