0,3

Comment from Michel ten Voorde (seqfan(AT)tenvoorde.org) Jun 20 2001: Consider 'triangles' with lengths n X n, constructed of unit squares. Then a(n) is the minimal number of squares (of any size) whose union is the triangle. The triangle for n=4 is

.__.__.__.__

|1.|2.|3.|4.|

|__|__|__|__|

...|5.|6.|7.|

...|__|__|__|

......|8.|9.|

......|__|__|

.........|10|

.........|__|

The minimal number of squares to cover this is 7, namely square 3-4-6-7, square 1, square 2, square 5, square 8, square 9 and square 10.

For n>0: replace all 0's by 1's in binary representation of n. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 14 2003

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences

R. Zumkeller, Logical Convolutions

a(n)=a(n-1)+n*(1-floor(a(n-1)/n)). If 2^(k-1)<= n < 2^k, a(n)=2^k-1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 25 2002

a(n)=1+2*a(floor(n/2)) for n>0. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 04 2003

G.f.: 1/(1-x) * sum_{k>=0} 2^k*x^2^k. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 18 2003

a(n) = 2*A053644(n)-1 = A091940(n) + A053644(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 15 2004

a(n) = OR{k OR (n-k): 0<=k<=n}. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 15 2008

Equals A062383(n)-1.

This is Guy Steele's sequence GS(6, 6) (see A135416).

Cf. A000004, A142149, A086099, A142150, A142151, A001477.

Sequence in context: A161771 A160515 A105670 this_sequence A092474 A107470 A071042

Adjacent sequences: A003814 A003815 A003816 this_sequence A003818 A003819 A003820

nonn,base

Marc LeBrun (mlb(AT)well.com)