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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A079408 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, T(m-1, n)) + T(m-1, n - T(m-1, n-1)) if m > 0.

Original entry on oeis.org

1, 1, 0, 3, 2, 0, 6, 2, 1, 0, 12, 6, 3, 1, 0, 24, 12, 6, 3, 1, 0, 48, 24, 12, 6, 3, 1, 0, 96, 48, 24, 12, 5, 3, 1, 0, 192, 96, 48, 24, 12, 6, 3, 1, 0, 384, 192, 96, 48, 24, 12, 6, 3, 1, 0, 768, 384, 192, 96, 48, 24, 12, 6, 3, 1, 0, 1536, 768, 384, 192, 96, 48, 24, 12, 6, 3, 1, 0, 3072, 1536
Offset: 0

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Author

Rob Arthan, Jan 06 2003

Keywords

Comments

This two-dimensional array is to Pascal's triangle as sequence A004001 is to Fibonacci's sequence. The sequence gives the values for nonnegative n read by antidiagonals. For negative n, T(0, n) = 0 and T(m, n) = T(m, 0) for m > 0.
Unlike A004001 this sequence admits a simple closed form: T(1, n) = 1 if n != 1, T(1, 1) = 2, T(m, n) = 3*2^(m-2) if m > 1, n != 3*2^(m-2) - 2, T(m, 3*2^(m-2) - 2) = 3*2^(m-2) - 1 if m > 1.

Examples

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

Crossrefs

Cf. A004001, A005185, A007318, A052553, A079409.
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