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A033581 6*n^2. 38
0, 6, 24, 54, 96, 150, 216, 294, 384, 486, 600, 726, 864, 1014, 1176, 1350, 1536, 1734, 1944, 2166, 2400, 2646, 2904, 3174, 3456, 3750, 4056, 4374, 4704, 5046, 5400, 5766, 6144, 6534, 6936, 7350, 7776, 8214, 8664, 9126, 9600, 10086, 10584, 11094, 11616 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of edges of a complete 4-partite graph of order 4n, K_n,n,n,n. - Roberto E. Martinez II, Oct 18 2001

Number of edges of the complete bipartite graph of order 7n, K_n,6n - Roberto E. Martinez II, Jan 07 2002

Number of edges in the line graph of the product of two cycle graphs, each of order n, L(C_n x C_n) - Roberto E. Martinez II, Jan 07 2002

Total surface area of a cube of edge length n. See A000578 for cube volume. See A070169 and A071399 for surface area and volume of a regular tetrahedron and links for the other Platonic solids. - Rick L. Shepherd, Apr 24 2002

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

Sequence found by reading the line from 0, in the direction 0, 6,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A003154 in the same spiral. - Omar E. Pol, Sep 08 2011

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Wolfram MathWorld, Platonic Solid

FORMULA

a(n) = A000290(n)*6. [From Omar E. Pol, Dec 11 2008]

a(n) = A001105(n)*3 = A033428(n)*2. [From Omar E. Pol, Dec 13 2008]

a(n) = 12*n+a(n-1)-6, and a(0)=0. [From Vincenzo Librandi, Aug 05 2010]

G.f.: 6*x*(1+x)/(1-x)^3. [Colin Barker, Feb 14 2012]

EXAMPLE

Contribution from Omar E. Pol, Aug 21 2011 (Start):

Illustration of initial terms as concentric hexagons:

.

.                                 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

.

.    6            24                   54

.

(End)

MAPLE

seq(6*n^2, n=0..44); # Nathaniel Johnston, Jun 26 2011

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +6; AppendTo[lst, s], {n, 0, 7!, 12}]; lst [From Vladimir Orlovsky, Nov 16 2008]

CROSSREFS

Cf. A000217, A000290, A033583, A033428.

Central column of triangle A001283.

Cf. A001105. [From Omar E. Pol, Dec 13 2008]

Cf. A085250, A152734, A152751. Bisection of A032528. - Omar E. Pol, Aug 20 2011

Sequence in context: A083170 A087081 A089973 * A213393 A009943 A028595

Adjacent sequences:  A033578 A033579 A033580 * A033582 A033583 A033584

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Nov 08 2001

STATUS

approved

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Last modified April 16 06:49 EDT 2014. Contains 240549 sequences.