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A105158 Table T(n,k), read by downward antidiagonals, defined by : T(0,0) = 0, T(n,n) = 2^n for n>0, T(n,k) - T(n,n) = A102371(n - k) if 0<= k < n, T(n,k) - T(n,n) = A102370(k - n) if k >= n. 0

%I #11 Sep 08 2013 19:54:50

%S 0,3,3,6,2,6,5,5,5,15,4,8,4,28,15,7,7,9,23,61,10,6,10,8,18,44,126,9,

%T 17,9,11,17,39,93,251,8,12,8,14,16,34,76,190,504,11,11,19,13,19,33,71,

%U 157,379,1017,14,10,14,12,22,32,66,140,318,760,2042,13,13,13,23,21,35,65

%N Table T(n,k), read by downward antidiagonals, defined by : T(0,0) = 0, T(n,n) = 2^n for n>0, T(n,k) - T(n,n) = A102371(n - k) if 0<= k < n, T(n,k) - T(n,n) = A102370(k - n) if k >= n.

%C Consider T(0,0) and the 2^n -1 first terms of the row n for n>0; this give A102370 : 0; 3; 6, 5, 4; 15, 10, 9, 8, 11, 14, 13; 28, 23, 18, 17, 16, 19, 22, 21, 20, 31, 26, 25, 24, 27, 30; ...

%H 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>].

%F T(0, k) = A102370(k); T(n, 0) = A103529(n+1).

%e Table T(n,k) begins:

%e 0, 3, 6, 5, 4, 15, 10, 9, 8, 11, 14, 13, 28, ...

%e 3, 2, 5, 8, 7, 6, 17, 12, 11, 10, 13, 16, 15, ...

%e 6, 5, 4, 7, 10, 9, 8, 19, 14, 13, 12, 15, 18, ...

%e 15, 10, 9, 8, 11, 14, 13, 12, 23, 18, 17, 16, 19, ...

%e 28, 23, 18, 17, 16, 19, 22, 21, 20, 31, 26, 25, 24, ...

%Y Cf. A102370, A102371, A103529.

%K nonn,tabl,base

%O 0,2

%A _Philippe Deléham_, May 01 2005

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