cp's OEIS Frontend

A239906 Let cn(n,k) denote the number of times 11..1 (k 1's) appears in the binary representation of n; a(n) = n - cn(n,1) + cn(n,2) - cn(n,3).

%I A239906 #13 Oct 06 2015 18:19:26
%S A239906 0,0,1,2,3,3,5,5,7,7,8,9,11,11,12,12,15,15,16,17,18,18,20,20,23,23,24,
%T A239906 25,26,26,27,27,31,31,32,33,34,34,36,36,38,38,39,40,42,42,43,43,47,47,
%U A239906 48,49,50,50,52,52,54,54,55,56,57,57,58,58,63,63,64,65,66,66,68,68,70,70,71,72,74,74
%N A239906 Let cn(n,k) denote the number of times 11..1 (k 1's) appears in the binary representation of n; a(n) = n - cn(n,1) + cn(n,2) - cn(n,3).
%H A239906 Michael De Vlieger, <a href="/A239906/b239906.txt">Table of n, a(n) for n = 0..10000</a>
%p A239906 # From A014081:
%p A239906 cn := proc(v, k) local n, s, nn, i, j, som, kk;
%p A239906 som := 0;
%p A239906 kk := convert(cat(seq(1, j = 1 .. k)), string);
%p A239906 n := convert(v, binary);
%p A239906 s := convert(n, string);
%p A239906 nn := length(s);
%p A239906 for i to nn - k + 1 do
%p A239906 if substring(s, i .. i + k - 1) = kk then som := som + 1 fi od;
%p A239906 som; end;
%p A239906 [seq(n-cn(n,1)+cn(n,2)-cn(n,3), n=0..100)];
%t A239906 cn[n_, k_] := Count[Partition[IntegerDigits[n, 2], k, 1], Table[1, {k}]]; Table[n - Sum[cn[n, i], {i, 1, 3, 2}] + cn[n, 2], {n, 0, 77}] (* _Michael De Vlieger_, Sep 18 2015 *)
%o A239906 (PARI)
%o A239906 a(n) = {
%o A239906     my(x = bitand(n, n>>1), wt = k->hammingweight(k));
%o A239906     n - wt(n) + wt(x) - wt(bitand(x, n>>2));
%o A239906 };
%o A239906 vector(78, i, a(i-1))  \\ _Gheorghe Coserea_, Sep 24 2015
%Y A239906 Cf. A000120, A012081, A014082, A239904, A239907.
%K A239906 nonn,base
%O A239906 0,4
%A A239906 _N. J. A. Sloane_, Apr 07 2014