0,2

The number of edges of a complete tripartite graph of order 3n, K_n,n,n. - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Oct 18 2001

Write 1,2,3,4,... in a hexagonal spiral around 0, then a(n) is the sequence found by reading the line from 0 in the direction 0,3,... - Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001. The spiral begins:

......16..15..14

....17..5...4...13

..18..6...0...3...12

19..7...1...2...11..26

..20..8...9...10..25

....21..22..23..24

Number of edges of the complete bipartite graph of order 4n, K_n,3n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002

Also the number of partitions of 6n + 3 into at most 3 parts.- R. K. Guy, Oct 23, 2003

Number of permutations of 3 distinct letters (ABC) each with n copies such that 3n-2 remain fixed points. E.g. if AAAAABBBBBCCCCC (3*5=15 letters) then 15-2=13 fixed points n5=75 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 02 2006

Numbers n such that the imaginary quadratic field Q[Sqrt[ -n]] has six units. - Marc LeBrun (mlb(AT)well.com), Apr 12 2006

The denominators of Hoehn's sequence (recalled by G. L. Honaker, Jr.) and the numerators of that sequence reversed. The sequence is 1/3, (1+3)/(5+7), (1+3+5)/(7+9+11), (1+3+5+7)/(9+11+13+15), . . . ; reduced to 1/3, 4/12, 9/27, 16/48, . . . . For the reversal, the reduction is 3/1, 12/4, 27/9, 48/16, . . . . - Enoch Haga (Enokh(AT)comcast.net), Oct 05 2007

3 times the squares. [From Omar E. Pol (info(AT)polprimos.com), Dec 11 2008]

Index entries for sequences related to linear recurrences with constant coefficients

F. Ellermann, Illustration of binomial transforms

Eric Weisstein's World of Mathematics, Unit

E. Weisstein, Numbers of units in imaginary quadratic fields

a(n)= A049452(n)-A049450(n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007

Right edge of the triangle in A132111: a(n)=A132111(n,n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 10 2007

G.f.: 3x(1+x)/(1-x)^3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2008]

a(n)=6*n+a(n-1)-9 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]

For n=2, a(2)=6*2+0-9=3; n=3, a(3)=6*3+3-9=12; n=4, a(4)=6*4+12-9=27 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]

seq(n*(6*n-1)-n*(3*n-1), n=0..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007

s=0; lst={s}; Do[s+=n++ +3; AppendTo[lst, s], {n, 0, 6!, 6}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]

(PARI) a(n)=3*n^2

Cf. A000567, A000217, A000290, A033581, A033583.

a(n)=3*A000290(n)

Cf. A033581.

Cf. A000290, A092205, A092206.

Cf. A000290.

Sequence in context: A125614 A061936 A074630 this_sequence A018230 A058034 A009259

Adjacent sequences: A033425 A033426 A033427 this_sequence A033429 A033430 A033431

nonn

Jeff Burch (jmburch(AT)osprey.smcm.edu)

Better description from N. J. A. Sloane (njas(AT)research.att.com) 5/98.