|
Search: id:A028896
|
|
|
| A028896 |
|
6 times triangular numbers: a(n) = 3*n*(n+1). |
|
+0
13
|
|
| 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; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
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 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).
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]
|
|
LINKS
|
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
|
|
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)-6 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
|
|
EXAMPLE
|
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]
|
|
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
|
|
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]
|
|
CROSSREFS
|
Cf. A000567.
Cf. A003215, A028895, A024966.
Cf. A084939, A084940, A084941, A084942, A084943, A084944.
Cf. A028895, A046092, A045943, A002378.
Cf. A049598, A124080, A046092, A033996, A002378.
Cf. A000217. [From Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
Sequence in context: A111147 A152539 A069958 this_sequence A034857 A116367 A101853
Adjacent sequences: A028893 A028894 A028895 this_sequence A028897 A028898 A028899
|
|
KEYWORD
|
nonn,easy,new
|
|
AUTHOR
|
Joe Keane (jgk(AT)jgk.org)
|
|
|
Search completed in 0.007 seconds
|
