%I #9 Oct 06 2021 08:31:43
%S 0,0,1,0,1,1,1,0,1,1,2,1,2,1,1,0,1,2,2,1,2,1,2,1,2,1,2,1,2,2,1,0,2,1,
%T 2,2,2,1,3,1,2,3,2,1,2,2,2,1,2,2,2,1,2,3,3,1,3,1,2,3,2,1,2,0,2,2,2,1,
%U 4,1,2,2,2,2,4,1,2,3,2,1,3,2,2,3,2,2,3,1,2,3,2,1,2,2,3,1,2,2,2,2,2,3,2,1,4
%N Number of partitions of n into consecutive parts containing no binary powers.
%C a(n) <= A001227(n).
%e a(60) = #{10+11+12+13+14, 19+20+21, 60} = 3, 4+5+6+7+8+9+10+11=60 doesn't count because 4=2^2 or 8=2^3.
%t a[n_] := a[n] = Count[IntegerPartitions[n, All, Cases[Range[3, n], k_Integer /; Total[IntegerDigits[k, 2]] > 1]], q_List /; Length[q] == Length[Union[q]] && Length[q] == First[q] - Last[q] + 1];
%t Table[Print[n, " ", a[n]]; a[n], {n, 1, 105}] (* _Jean-François Alcover_, Oct 06 2021 *)
%Y Cf. A001227, A118164.
%K nonn
%O 1,11
%A _Reinhard Zumkeller_, Apr 17 2006
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