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%I #20 Aug 27 2024 04:28:03
%S 1,1,1,1,3,1,1,2,2,1,1,6,5,6,1,1,7,15,15,7,1,1,5,8,30,8,5,1,1,4,31,50,
%T 50,31,4,1,1,12,18,36,101,36,18,12,1,1,13,54,126,65,65,126,54,13,1,1,
%U 15,59,68,187,130,187,68,59,15,1
%N Gray code applied to Pascal's triangle: T(n,k) = GrayCode(binomial(n, k)).
%H G. C. Greubel, <a href="/A143214/b143214.txt">Rows n = 1..50 of the triangle, flattened</a>
%H Eric Weisstein, <a href="http://mathworld.wolfram.com/notebooks/Combinatorics/GrayCode.nb">Mathematica Notebook GrayCode.nb</a>
%H Eric Weisstein, <a href="http://mathworld.wolfram.com/GrayCode.html">Gray Code</a>, MathWorld.
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 3, 1;
%e 1, 2, 2, 1;
%e 1, 6, 5, 6, 1;
%e 1, 7, 15, 15, 7, 1;
%e 1, 5, 8, 30, 8, 5, 1;
%e 1, 4, 31, 50, 50, 31, 4, 1;
%e 1, 12, 18, 36, 101, 36, 18, 12, 1;
%e 1, 13, 54, 126, 65, 65, 126, 54, 13, 1;
%e 1, 15, 59, 68, 187, 130, 187, 68, 59, 15, 1;
%t GrayCode[n_, k_]:= FromDigits[BitXor@@@Partition[Prepend[IntegerDigits[n, 2, k], 0], 2, 1], 2];
%t A143214[n_, k_]:= GrayCode[Binomial[n-1, k-1], 10];
%t Table[A143214[n,k], {n,12}, {k,n}]//Flatten
%Y Cf. A143213.
%K nonn,tabl
%O 1,5
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 20 2008
%E Edited by _Michel Marcus_ and _Joerg Arndt_, Apr 22 2013
%E Edited by _G. C. Greubel_, Aug 27 2024
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