A064201 9 times octagonal numbers: a(n) = 9*n*(3*n-2).

0, 9, 72, 189, 360, 585, 864, 1197, 1584, 2025, 2520, 3069, 3672, 4329, 5040, 5805, 6624, 7497, 8424, 9405, 10440, 11529, 12672, 13869, 15120, 16425, 17784, 19197, 20664, 22185, 23760, 25389, 27072, 28809, 30600, 32445, 34344, 36297, 38304, 40365, 42480, 44649

Offset: 0

Author

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Sep 22 2001

Keywords

• nonn
• easy

References

• L. Berzolari, Allgemeine Theorie der Höheren Ebenen Algebraischen Kurven, Encyclopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Band III_2. Heft 3, Leipzig: B. G. Teubner, 1906. p. 341.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000567, A152751.

Programs

Mathematica

9*PolygonalNumber[8,Range[0,40]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3,-3,1},{0,9,72},40] (* Harvey P. Dale, Aug 01 2020 *)

PARI

a(n)=9*n*(3*n-2) \\ Charles R Greathouse IV, Jun 16 2017

Formula

a(n) = 9*(n-2)*(3*n-8), with offset 2.

a(n) = 9*A000567(n). - Omar E. Pol, Dec 11 2008

a(n) = a(n-1) + 54*n - 45, with n > 0, a(0)=0. - Vincenzo Librandi, Dec 15 2010

G.f.: 9*x*(1+5*x)/(1-x)^3. - Colin Barker, Feb 29 2012

From Elmo R. Oliveira, Dec 25 2024: (Start)

E.g.f.: 9*exp(x)*x*(1 + 3*x).

a(n) = 3*A152751(n).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)

Extensions

Better definition, corrected offset and edited from Omar E. Pol, Dec 11 2008