A061290 - OEIS

%I #8 Oct 27 2018 21:58:19

%S 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,

%T 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,

%U 0,0,1,5,16,42,120,247,511,1024,0,0,0,0,5,16,42,99,247,502,1023,2048,0,0

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

%C Row sums give 3^n.

%F 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)).

%e 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.

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

%K nonn,tabl

%O 0,3

%A _Henry Bottomley_, May 22 2001