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A079409
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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.
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1
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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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.
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EXAMPLE
| 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
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CROSSREFS
| Cf. A004001, A005185, A007318, A052553, A079408.
Sequence in context: A064559 A067255 A065716 * A114643 A038498 A184154
Adjacent sequences: A079406 A079407 A079408 * A079410 A079411 A079412
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KEYWORD
| nonn,tabl
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AUTHOR
| Rob Arthan (rda(AT)lemma-one.com), Jan 06 2003
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