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%I #12 Feb 07 2020 20:49:08
%S 1,2,2,1,2,1,3,3,3,3,2,3,1,3,2,2,4,6,6,4,2,1,3,3,3,3,3,1,4,4,3,7,7,3,
%T 4,4,3,4,1,6,4,6,1,4,3,3,6,10,10,6,6,10,10,6,3,2,4,6,4,4,3,4,4,6,4,2,
%U 3,6,6,9,11,4,4,11,9,6,6,3,2,4,3,7,8,10,1
%N Square array T(n, k) read by antidiagonals, n > 0 and k > 0: T(n, k) is the number of distinct shuffles of the words corresponding to the binary representations of n and of k.
%C A shuffle of two words is formed by interspersing their characters into a new word, keeping the characters of each word in order. Leading zeros are ignored.
%H Rémy Sigrist, <a href="/A303476/a303476.txt">C++ program for A303476</a>
%F T(n, k) = T(k, n).
%F T(n, n) = A193020(n).
%F Apparently T(n, 1) = A008687(n + 1).
%F T(2^i, 2^j) = 1 + max(i, j) for any i >=0 and j >= 0.
%F T(n, k) = 1 iff n = 2^i - 1 and k = 2^j - 1 for some i > 0 and j > 0.
%F T(2^i, 2^j - 1) = binomial(i + j, j) for any i >= 0 and j > 0.
%e Array T(n, k) begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12
%e ---+------------------------------------------------
%e 1| 1 2 1 3 2 2 1 4 3 3 2 3
%e 2| 2 2 3 3 4 3 4 4 6 4 6 4
%e 3| 1 3 1 6 3 3 1 10 6 6 3 6
%e 4| 3 3 6 3 7 6 10 4 9 7 13 6
%e 5| 2 4 3 7 4 6 4 11 8 8 6 10
%e 6| 2 3 3 6 6 3 4 10 12 7 9 6
%e 7| 1 4 1 10 4 4 1 20 10 10 4 10
%e 8| 4 4 10 4 11 10 20 4 13 11 24 10
%e 9| 3 6 6 9 8 12 10 13 9 15 14 18
%e 10| 3 4 6 7 8 7 10 11 15 8 14 11
%o (C++) See Links section.
%Y Cf. A008687, A193020.
%K nonn,base,tabl
%O 1,2
%A _Rémy Sigrist_, Apr 24 2018