A079409 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.

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, 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, 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

Offset: 0

Author

Rob Arthan, Jan 06 2003

Keywords

• nonn
• tabl

Comments

This two-dimensional array is to Pascal's triangle as the Hofstadter Q-sequence A005185 is to Fibonacci's sequence.

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.

Examples

			For 0 <= m <= 6 and 0 <= n <= 6, the array looks like:
1,0,0,0,0,0,0
1,1,0,0,0,0,0
1,2,1,0,0,0,0
1,1,3,1,0,0,0
1,2,1,4,1,0,0
1,1,3,1,5,1,0
1,2,1,4,1,6,1
		

Crossrefs

Cf. A004001, A005185, A007318, A052553, A079408.