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%I #4 Feb 18 2015 07:51:27
%S 1,1,0,1,1,0,1,2,0,0,1,1,1,0,0,1,2,3,0,0,0,1,1,1,1,0,0,0,1,2,3,4,0,0,
%T 0,0,1,1,1,1,1,0,0,0,0,1,2,3,4,5,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,1,2,
%U 3,4,5,6,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,2,3,4,5,6,7,0,0,0,0,0,0,0
%N Array T(m,n) (m>=0, n>=0) read by antidiagonals: T(0, 0) = 1, T(0, n) = 0 if n > 0, T(m, n) = T(m-1, n - T(m-1, n)) + T(m-1, n - T(m-1, n-1)) if m > 0.
%C This two-dimensional array is to Pascal's triangle as the Hofstadter Q-sequence A005185 is to Fibonacci's sequence.
%C Unlike the Hofstadter Q-sequence, it is very regular and admits a simple closed form: T(m, n) = 0 if n > m, T(m, n) = 1 if n <= m and m - n is even, T(m, n) = n + 1 if n <= m and m - n is odd.
%e For 0 <= m <= 6 and 0 <= n <= 6, the array looks like:
%e 1,0,0,0,0,0,0
%e 1,1,0,0,0,0,0
%e 1,2,1,0,0,0,0
%e 1,1,3,1,0,0,0
%e 1,2,1,4,1,0,0
%e 1,1,3,1,5,1,0
%e 1,2,1,4,1,6,1
%Y Cf. A004001, A005185, A007318, A052553, A079408.
%K nonn,tabl
%O 0,8
%A _Rob Arthan_, Jan 06 2003
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