A152751 3 times octagonal numbers: a(n) = 3*n*(3*n-2).

0, 3, 24, 63, 120, 195, 288, 399, 528, 675, 840, 1023, 1224, 1443, 1680, 1935, 2208, 2499, 2808, 3135, 3480, 3843, 4224, 4623, 5040, 5475, 5928, 6399, 6888, 7395, 7920, 8463, 9024, 9603, 10200, 10815, 11448, 12099, 12768, 13455, 14160, 14883, 15624, 16383, 17160

Offset: 0

Author

Omar E. Pol, Dec 12 2008

Keywords

• easy
• nonn

Comments

a(n) also can be represented as n concentric triangles (see example). - Omar E. Pol, Aug 21 2011

Examples

			From _Omar E. Pol_, Aug 21 2011: (Start)
Illustration of initial terms as concentric triangles:
.
.                                          o
.                                         o o
.                                        o   o
.                                       o     o
.                 o                    o   o   o
.                o o                  o   o o   o
.               o   o                o   o   o   o
.              o     o              o   o     o   o
.    o        o   o   o            o   o   o   o   o
.   o o      o   o o   o          o   o   o o   o   o
.           o           o        o   o           o   o
.          o o o o o o o o      o   o o o o o o o o   o
.                              o                       o
.                             o o o o o o o o o o o o o o
.
.    3            24                       63
(End)
		

Links

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

Crossrefs

Cf. A000567, A064201, A139267, A152995.

3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152759, A152767, A153783, A153448, A153875.

Cf. A033581, A085250, A152734, A194273. - Omar E. Pol, Aug 21 2011

Cf. numbers of the form n*(n*k - k + 6)/2, this sequence is the case k=18: see Comments lines of A226492.

Programs

Mathematica

s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,3,6!,18}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
3*PolygonalNumber[8,Range[0,40]] (* Harvey P. Dale, May 08 2022 *)

PARI

a(n)=3*n*(3*n-2) \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = 9*n^2 - 6*n = 3*A000567(n) = A064201(n)/3.

a(n) = a(n-1) + 18*n - 15 with n > 0, a(0)=0. - Vincenzo Librandi, Nov 26 2010

G.f.: 3*x*(1+5*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011

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

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

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

a(n) = n + A152995(n). (End)