A061290 Square array read by antidiagonals of T(n,k) = T(n-1,k) + T(n-1, floor(k/2)) with T(0,0)=1.

1, 0, 2, 0, 1, 4, 0, 0, 3, 8, 0, 0, 1, 7, 16, 0, 0, 1, 4, 15, 32, 0, 0, 0, 4, 11, 31, 64, 0, 0, 0, 1, 11, 26, 63, 128, 0, 0, 0, 1, 5, 26, 57, 127, 256, 0, 0, 0, 1, 5, 16, 57, 120, 255, 512, 0, 0, 0, 1, 5, 16, 42, 120, 247, 511, 1024, 0, 0, 0, 0, 5, 16, 42, 99, 247, 502, 1023, 2048, 0, 0

Offset: 0

Author

Henry Bottomley, May 22 2001

Keywords

• nonn
• tabl

Comments

Row sums give 3^n.

Examples

			T(9,3) = T(8,3) + T(8,floor(3/2)) = T(8,3) + T(8,1) = 247 + 255 = 502. Rows start (1,0,0,0,0,...), (2,1,0,0,0,...), (4,3,1,1,0,...), (8,7,4,4,1,...), etc.
		

Crossrefs

Row sums are A000244. Columns are A000079, A000225, A000295 twice, A002662 four times, A002663 eight times, A002664 sixteen times, A035038 thirty two times, etc.

Formula

T(n, k) = C(n, 0) + C(n, 1) + ... + C(n, n-ceiling(log_2(k+1))) = 2^n - C(n, 0) - C(n, 1) - ... - C(n, floor(log_2(k))) = A008949(n, n-A029837(k+1)) = A000079(n) - A008949(n, A000523(k)).