Search: id:A028896
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%I A028896
%S A028896 0,6,18,36,60,90,126,168,216,270,330,396,468,546,630,720,816,918,
%T A028896 1026,1140,1260,1386,1518,1656,1800,1950,2106,2268,2436,2610,2790,
%U A028896 2976,3168,3366,3570,3780,3996,4218,4446,4680,4920,5166,5418,5676
%N A028896 6 times triangular numbers: a(n) = 3*n*(n+1).
%C A028896 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 0,6,... - Floor 
               van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001. The spiral begins:
%C A028896 ......16..15..14
%C A028896 ....17..5...4...13
%C A028896 ..18..6...0...3...12
%C A028896 19..7...1...2...11..26
%C A028896 ..20..8...9...10..25
%C A028896 ....21..22..23..24
%C A028896 If Y is a 4-subset of an n-set X then, for n>=5, a(n-5) is the number 
               of (n-4)-subsets of X having exactly two elements in common with 
               Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007
%C A028896 Comment from Terry Stickels (Terrystickels(AT)aol.com), Jul 12 2008: 
               a(n) is the maximal number of points of interesction of n+1 distinct 
               triangles drawn in the plane. For example, two triangles can interesect 
               in at most a(1) = 6 points (as illustrated in the Star of David configuration).
%C A028896 Except for the first term, a(n)=6*n+a(n-1), (with a(1)=6) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
%H A028896 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%F A028896 G.f.: A(x) = 6*x/(1-x)^3.
%F A028896 Polygorial(3, n+1) - Daniel Dockery (peritus(AT)gmail.com) Jun 16, 2003
%F A028896 a(n)=A049598/2; a(n)=A124080-A046092; a(n)=A033996-A002378. - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Mar 06 2007
%F A028896 a(n) = 3n^2 + 3n = A000217(n)*6 = A002378(n)*3 = A045943(n)*2. [From 
               Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
%F A028896 a(n)=6*n+a(n-1)-6 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 08 2009]
%e A028896 For n=2, a(2)=6*2+0-6=6; n=3, a(3)=6*3+6-6=18; n=4, a(4)=6*4+18-6=36 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
%p A028896 [seq(6*binomial(n,2),n=1..44)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 24 2006
%p A028896 a:=n->sum(sum(3, j=1..n), k=0..n): seq(a(n), n=0..43); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), May 30 2007
%t A028896 s=0;lst={s};Do[s+=n++ +6;AppendTo[lst, s], {n, 0, 7!, 6}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
%Y A028896 Cf. A000567.
%Y A028896 Cf. A003215, A028895, A024966.
%Y A028896 Cf. A084939, A084940, A084941, A084942, A084943, A084944.
%Y A028896 Cf. A028895, A046092, A045943, A002378.
%Y A028896 Cf. A049598, A124080, A046092, A033996, A002378.
%Y A028896 Cf. A000217. [From Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
%Y A028896 Sequence in context: A111147 A152539 A069958 this_sequence A034857 A116367 
               A101853
%Y A028896 Adjacent sequences: A028893 A028894 A028895 this_sequence A028897 A028898 
               A028899
%K A028896 nonn,easy,new
%O A028896 0,2
%A A028896 Joe Keane (jgk(AT)jgk.org)

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