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A143261 Triangle read by rows: binary reversed Gray code of binomial(n,m).

%I A143261 #21 Feb 16 2025 08:33:08
%S A143261 1,1,1,1,3,1,1,1,1,1,1,3,5,3,1,1,7,15,15,7,1,1,5,1,15,1,5,1,1,1,31,19,
%T A143261 19,31,1,1,1,3,9,9,83,9,9,3,1,1,11,27,63,65,65,63,27,11,1,1,15,55,17,
%U A143261 221,65,221,17,55,15,1,1,7,13,239,495,297,297,495,239,13,7,1
%N A143261 Triangle read by rows: binary reversed Gray code of binomial(n,m).
%C A143261 Row sums are: 1, 2, 5, 4, 13, 46, 29, 104, 127, 334, 683, 2104,...
%H A143261 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/GrayCode.html">Gray code</a>
%F A143261 T(n,m) = A030101(A003188(binomial(n,m))) = A030101(A143214(n,m)). - _R. J. Mathar_, Mar 10 2015
%e A143261 1;
%e A143261 1, 1;
%e A143261 1, 3, 1;
%e A143261 1, 1, 1, 1;
%e A143261 1, 3, 5, 3, 1;
%e A143261 1, 7, 15, 15, 7, 1;
%e A143261 1, 5, 1, 15, 1, 5, 1;
%e A143261 1, 1, 31, 19, 19, 31, 1, 1;
%e A143261 1, 3, 9, 9, 83, 9, 9, 3, 1;
%e A143261 1, 11, 27, 63, 65, 65, 63, 27, 11, 1;
%e A143261 1, 15, 55, 17, 221, 65, 221, 17, 55, 15, 1;
%e A143261 1, 7, 13, 239, 495, 297, 297, 495, 239, 13, 7, 1;
%p A143261 A143261 := proc(n,m)
%p A143261     binomial(n,m) ;
%p A143261     A003188(%) ;
%p A143261     A030101(%) ;
%p A143261 end proc: # _R. J. Mathar_, Mar 10 2015
%t A143261 GrayCodeList[k_] := Module[{b = IntegerDigits[k, 2], i}, Do[ If[b[[i - 1]] == 1, b[[i]] = 1 - b[[i]]], {i, Length[b], 2, -1} ]; b ]; b = Table[Table[Sum[GrayCodeList[Binomial[n, k]][[m + 1]]*2^m, {m, 0, Length[GrayCodeList[Binomial[n, k]]] - 1}], {k, 0, n}], {n, 0, Length[a]}]; Flatten[b]
%Y A143261 Cf. A143214, A178058.
%K A143261 nonn,tabl
%O A143261 0,5
%A A143261 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 21 2008
%E A143261 Edited by _R. J. Mathar_, Mar 10 2015