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URL: https://oeis.org/A261343

⇱ A261343 - OEIS

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A261343
50-gonal numbers: a(n) = 48*n*(n-1)/2 + n.
1
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
0,3
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.
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
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 *)
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