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.

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

0,4

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.

Links

Table of n, a(n) for n=0..79.

Example

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.

Sequence in context: A364361 A338022 A253176 * A114376 A216395 A058096

Adjacent sequences: A079405 A079406 A079407 * A079409 A079410 A079411

Keyword

nonn,tabl

Author

Rob Arthan, Jan 06 2003

Status

approved