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A227193
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Difference of (product of runlengths of 1-bits) and (product of runlengths of 0-bits) in binary representation of n.
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3
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0, 0, 0, 1, -1, 0, 1, 2, -2, -1, 0, 1, 0, 1, 2, 3, -3, -2, -1, 0, -1, 0, 1, 2, -1, 0, 1, 3, 1, 2, 3, 4, -4, -3, -2, -1, -3, -1, 0, 1, -2, -1, 0, 1, 0, 1, 2, 3, -2, -1, 0, 2, 0, 1, 3, 5, 0, 1, 2, 5, 2, 3, 4, 5, -5, -4, -3, -2, -5, -2, -1, 0, -5, -3, -1, 0, -2, 0
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OFFSET
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0,8
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COMMENTS
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The sequence seems to consist of palindromic subsequences centered around each (2^k)-1 and 2^k (with end points near the terms of A000975), which is easily explained by symmetric pairing of binary expansion of n and its complement.
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LINKS
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FORMULA
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MAPLE
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a:= proc(n) local i, j, m, r, s; m, r, s:= n, 1, 1;
while m>0 do
for i from 0 while irem(m, 2, 'h')=0 do m:=h od;
for j from 0 while irem(m, 2, 'h')=1 do m:=h od;
r, s:= r*j, s*max(i, 1)
od; r-s
end:
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MATHEMATICA
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a[n_] := With[{s = Split @ IntegerDigits[n, 2]}, Times @@ Length /@ Select[ s, First[#]==1&] - Times @@ Length /@ Select[s , First[#]==0&]]; Table[ a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 28 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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