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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
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
0,3
COMMENTS
Row sums give 3^n.
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)).
EXAMPLE
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.
Sequence in context: A258228 A271584 A072737 * A099096 A099089 A121298
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, May 22 2001
STATUS
approved