login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A152751 3 times octagonal numbers: 3*n*(3*n-2). 19
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

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

EXAMPLE

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)

MATHEMATICA

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 3, 6!, 18}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)

PROG

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

CROSSREFS

Cf. A000567, A064201, A139267.

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.

Sequence in context: A101008 A070734 A009113 * A162654 A092468 A027158

Adjacent sequences:  A152748 A152749 A152750 * A152752 A152753 A152754

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Dec 12 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 19 11:04 EST 2017. Contains 294936 sequences.