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)gmail.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

a(n) + A145919(3n+3) = 0. [From Matthew Vandermast (ghodges14(AT)comcast.net), Oct 28 2008]

Except for the first term, a(n)=3*n+a(n-1), (with a(1)=3) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 23 2009]

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

Alfred Hoehn, Illustration of initial terms of A000326, A005449, A045943, A115067

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

a(n)=3*n+a(n-1)-3 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]

For n=2, a(2)=3*2+0-3=3; n=3, a(3)=3*3+3-3=9; n=4, a(4)=3*4+9-3=18 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]

[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

a:=n->sum(n, k=0..n):seq(a(n)+sum(k, k=1..n), n=0..48); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 10 2008

with(finance):seq(add(cashflows([n, k, 0], 0 ), k=0..n), n=0..45); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]

s=0; lst={s}; Do[s+=n; s+=n+1; s+=n+2; AppendTo[lst, s], {n, 0, 6!, 1}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 31 2008]

s = 0; lst = {}; Do[s += n; AppendTo[lst, s], {n, 0, 160, 3}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]

Table[Sum[i + n - 3, {i, 3, n}], {n, 2, 50}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]

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

Cf. A051162.

The generalized pentagonal numbers b*n+3*n*(n-1)/2, for b = 1 through 12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140672, A140673, A140674, A140675, A151542.

Sequence in context: A159794 A100967 A134479 this_sequence A127759 A064843 A093446

Adjacent sequences: A045940 A045941 A045942 this_sequence A045944 A045945 A045946

nonn,new

R. K. Guy