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A143213 Triangle T(n,m) read by rows: Gray code of A060187(n, k) (decimal representation), 1 <= k <= n, n >= 1.

%I A143213 #24 Feb 16 2025 08:33:08
%S A143213 1,1,1,1,5,1,1,28,28,1,1,106,149,106,1,1,155,987,987,155,1,1,955,440,
%T A143213 514,440,955,1,1,194,137,974,974,137,194,1,1,340,754,60,293,60,754,
%U A143213 340,1,1,181,238,166,377,377,166,238,181,1,1,977,283,540,411,142,411,540,283,977,1
%N A143213 Triangle T(n,m) read by rows: Gray code of A060187(n, k) (decimal representation), 1 <= k <= n, n >= 1.
%H A143213 G. C. Greubel, <a href="/A143213/b143213.txt">Rows n = 1..50 of the triangle, flattened</a>
%H A143213 Eric Weisstein, <a href="https://mathworld.wolfram.com/notebooks/Combinatorics/GrayCode.nb">Mathematica Notebook GrayCode.nb</a>
%H A143213 Eric Weisstein, <a href="https://mathworld.wolfram.com/GrayCode.html">Gray Code</a>, MathWorld.
%F A143213 T(n, n-k) = T(n, k). - _G. C. Greubel_, Aug 08 2024
%e A143213 Triangle begins as:
%e A143213   1;
%e A143213   1,   1;
%e A143213   1,   5,   1;
%e A143213   1,  28,  28,   1;
%e A143213   1, 106, 149, 106,   1;
%e A143213   1, 155, 987, 987, 155,   1;
%e A143213   1, 955, 440, 514, 440, 955,   1;
%e A143213   1, 194, 137, 974, 974, 137, 194,   1;
%e A143213   1, 340, 754,  60, 293,  60, 754, 340,   1;
%e A143213   1, 181, 238, 166, 377, 377, 166, 238, 181,   1;
%e A143213   1, 977, 283, 540, 411, 142, 411, 540, 283, 977,  1;
%t A143213 GrayCode[n_, k_]:= FromDigits[BitXor@@@Partition[Prepend[IntegerDigits[n,2,k], 0], 2, 1], 2];
%t A143213 A060187[n_, k_]:= Sum[(-1)^(k-j)*Binomial[n,k-j]*(2*j-1)^(n-1), {j,k}];
%t A143213 A143213[n_, k_]:= GrayCode[A060187[n, k], 10];
%t A143213 Table[A143213[n,k], {n,12}, {k,n}]//Flatten
%Y A143213 Cf. A060187, A143214.
%K A143213 nonn,tabl
%O A143213 1,5
%A A143213 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 20 2008
%E A143213 Edited by _G. C. Greubel_, Aug 27 2024