0,2

In 24-bit RGB color cube, the number of color-lattice-points in r+g+b = n planes at n < 256 equals the triangular numbers. For n = 256, ..., 765 the number of legitimate color partitions is less than A000217(n) because {r,g,b} components cannot exceed 255. For n=256,..,511, the number of non-color partitions are computable with A045943(n-255), while for n = 512-765, the number of color points in r+g+b planes equals A000217(765-n). - Labos E. (labos(AT)ana.sote.hu), Jun 20 2005

a(n) = A126890(n+1,n-1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Dec 30 2006

If a 3-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then a(n-3) is the number of 3-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 19 2007

Labos E.: On the number of RGB-colors we can distinguish. Partition Spectra. Lecture at 7th Hungarian Conference on Biometry and Biomathematics. Budapest. Jul 06, 2005.

Milan Janjic, Two Enumerative Functions

a(n) is the sum of n+1 integers starting from n, i.e. 1+2, 2+3+4, 3+4+5+6, 4+5+6+7+8, etc. - Jon Perry (perry(AT)globalnet.co.uk), Jan 15 2004

[seq(3*binomial(n, 2) , n=1..49)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2006

a:=n->sum(3*j, j=0..n): seq(a(n), n=0..48); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007

a:=n->sum(n+j, j=1..n)+n: seq(a(n), n=0..48); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2007

3 times triangular numbers (A000217). Cf. A005448, A002378, A046092.

Cf. A051162.

Adjacent sequences: A045940 A045941 A045942 this_sequence A045944 A045945 A045946

Sequence in context: A103312 A100967 A134479 this_sequence A127759 A064843 A093446

nonn

R. K. Guy