A079408 - OEIS

%I #7 Jan 01 2024 13:30:59

%S 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,

%T 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,

%U 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

%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, 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 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.

%C 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.

%e For 0 <= m <= 3 and 0 <= n <= 5, the array of values looks like:

%e 1,0,0,0,0,0,0

%e 1,2,1,1,1,1,1

%e 3,2,3,3,3,3,3

%e 6,6,6,6,5,6,6

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

%K nonn,tabl

%O 0,4

%A _Rob Arthan_, Jan 06 2003