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A103842 Triangle read by rows: row n is binary expansion of 2^n-n, n >= 1.

%I A103842 #15 Feb 06 2022 14:49:54
%S A103842 1,1,0,1,0,1,1,1,0,0,1,1,0,1,1,1,1,1,0,1,0,1,1,1,1,0,0,1,1,1,1,1,1,0,
%T A103842 0,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,0,1,0,1,1,1,
%U A103842 1,1,1,1,1,1,0,1,0,0,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0
%N A103842 Triangle read by rows: row n is binary expansion of 2^n-n, n >= 1.
%C A103842 This sequence can also be obtained by reading (from bottom to top, column by column) the array given in A103582 after suppressing the terms below the main diagonal.
%H A103842 David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].
%H A103842 David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
%e A103842 Table begins:
%e A103842 1
%e A103842 1 0
%e A103842 1 0 1
%e A103842 1 1 0 0
%e A103842 1 1 0 1 1
%e A103842 1 1 1 0 1 0
%e A103842 1 1 1 1 0 0 1
%p A103842 p:=proc(n) local A,j,b: A:=convert(2^n-n,base,2): for j from 1 to nops(A) do b:=j->A[nops(A)+1-j] od: seq(b(j),j=1..nops(A)): end: for n from 1 to 15 do p(n) od; # yields sequence in triangular form # _Emeric Deutsch_, Apr 16 2005
%t A103842 Table[IntegerDigits[2^n-n,2],{n,20}]//Flatten (* _Harvey P. Dale_, Feb 06 2022 *)
%o A103842 (PARI) tabl(nn) = for (n=1, nn, print(binary(2^n-n))); \\ _Michel Marcus_, Mar 01 2015
%Y A103842 Cf. A000325, A103582.
%K A103842 nonn,tabl,easy
%O A103842 1,1
%A A103842 _Philippe Deléham_, Mar 31 2005
%E A103842 More terms from _Emeric Deutsch_, Apr 16 2005