A151843 a(0)=0; a(1)=0; a(2)=0; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=a(j) + a(j + 1) except we add 1 if j=2^i-1.

0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 1, 0, 1, 3, 3, 0, 0, 1, 1, 0, 1, 3, 2, 0, 1, 2, 1, 1, 4, 6, 4, 0, 0, 1, 1, 0, 1, 3, 2, 0, 1, 2, 1, 1, 4, 6, 3, 0, 1, 2, 1, 1, 4, 5, 2, 1, 3, 3, 2, 5, 10, 10, 5, 0, 0, 1, 1, 0, 1, 3, 2, 0, 1, 2, 1, 1, 4, 6, 3, 0, 1, 2, 1, 1, 4, 5, 2, 1, 3, 3, 2, 5, 10, 10, 4, 0, 1, 2, 1, 1, 4, 5

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

I would very much like a g.f. for this sequence!

Example

From Omar E. Pol, Jul 17 2009: (Start)
Triangle begins:
0;
0;
0,1;
0,0,1,2;
0,0,1,1,0,1,3,3;
0,0,1,1,0,1,3,2,0,1,2,1,1,4,6,4;
... (End)

Maple

M:=520;
f:=proc(r, s, a, b) local s1, n, i, j; global M;
s1:=array(0..M+10);
s1[0]:=r; s1[1]:=s;
for n from 2 to M do i:=floor(log(n)/log(2));
j:=n-2^i;
if (j=2^i-1) then s1[n]:=a*s1[j]+b*s1[j+1]+1 else
s1[n]:=a*s1[j]+b*s1[j+1]; fi;
od:
[seq(s1[n], n=0..M)];
end;
f(0, 0, 1, 1);

Mathematica

M = 520; f[r_, s_, a_, b_] := Module[{s1, n, i, j} , s1[0] = r; s1[1] = s; For[n = 2, n <= M, n++, i = Floor[Log[2, n]]; j = n - 2^i; If[j == 2^i - 1, s1[n] = a*s1[j]+b*s1[j+1]+1, s1[n] = a*s1[j]+b*s1[j+1]]];  Table[s1[n], {n, 0, M}]]; f[0, 0, 1, 1] (* Jean-François Alcover, Mar 03 2014, after Maple *)

Crossrefs

Cf. A151843-A151874.

Sequence in context: A025922 A342322 A161369 * A276422 A323069 A325334

Adjacent sequences: A151840 A151841 A151842 * A151844 A151845 A151846

Keyword

nonn,look

Author

N. J. A. Sloane, Jul 17 2009, Jul 19 2009

Status

approved