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A028896
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6 times triangular numbers: a(n) = 3*n*(n+1).
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14
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0, 6, 18, 36, 60, 90, 126, 168, 216, 270, 330, 396, 468, 546, 630, 720, 816, 918, 1026, 1140, 1260, 1386, 1518, 1656, 1800, 1950, 2106, 2268, 2436, 2610, 2790, 2976, 3168, 3366, 3570, 3780, 3996, 4218, 4446, 4680, 4920, 5166, 5418, 5676
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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:
......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
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
Comment from Terry Stickels (Terrystickels(AT)aol.com), Jul 12 2008: a(n) is the maximal number of points of intersection of n+1 distinct triangles drawn in the plane. For example, two triangles can intersect in at most a(1) = 6 points (as illustrated in the Star of David configuration).
Also sequence found by reading the line from 0, in the direction 0, 6,... and the same line from 0, in the direction 0, 18,..., in the square spiral whose vertices are the generalized octagonal numbers A001082. Axis perpendicular to A195143 in the same spiral. - Omar E. Pol, Sep 18 2011
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LINKS
| Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
| G.f.: A(x) = 6*x/(1-x)^3.
Polygorial(3, n+1) - Daniel Dockery (peritus(AT)gmail.com) Jun 16, 2003
a(n)=A049598/2; a(n)=A124080-A046092; a(n)=A033996-A002378. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 06 2007
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]
a(n)=6*n+a(n-1) (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 05 2010]
a(n) = A003215(n) - 1. - Omar E. Pol, Oct 03 2011
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EXAMPLE
| a(1)=6*1+0=6; a(2)=6*2+6=18; a(3)=6*3+18=36 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 05 2010]
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MAPLE
| [seq(6*binomial(n, 2), n=1..44)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2006
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
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MATHEMATICA
| 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]
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CROSSREFS
| Cf. A000567, A003215, A028895, A024966, A084939, A084940, A084941, A084942, A084943, A084944, A028895, A046092, A045943, A002378, A049598, A124080, A046092, A033996, A002378, A000217.
Sequence in context: A172522 A152539 A069958 * A034857 A116367 A180438
Adjacent sequences: A028893 A028894 A028895 * A028897 A028898 A028899
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KEYWORD
| nonn,easy
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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