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A151843
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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.
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32
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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LINKS
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FORMULA
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I would very much like a g.f. for this sequence!
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EXAMPLE
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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)
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MAPLE
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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);
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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