A038871 - OEIS

%I #9 Feb 18 2021 16:15:16

%S 0,1,1,3,1,5,7,1,5,11,15,1,9,21,27,31,1,9,21,43,55,63,1,17,37,85,91,

%T 119,127,1,17,73,85,171,219,239,255,1,33,73,165,341,363,439,495,511,1,

%U 33,137,293,341,683,731,887,991,1023,1,65,273,585,661,1365,1387

%N Triangle read by rows: T(n,k) = number of orbits of order k under doubling map which remain in a semicircle, with k dividing n.

%F Apparently T(n, k) = Sum_{j=0..n-1} 2^floor(n*j/k), for 0 <= k <= n - 2 with T(1,0)=0. - _Sean A. Irvine_, Feb 16 2021

%e From _Sean A. Irvine_, Feb 16 2021: (Start)

%e Triangle begins:

%e   0;

%e   1;

%e   1, 3;

%e   1, 5, 7;

%e   1, 5, 11, 15;

%e   1, 9, 21, 27, 31;

%e   1, 9, 21, 43, 55, 63;

%e   1, 17, 37, 85, 91, 119, 127;

%e   1, 17, 73, 85, 171, 219, 239, 255;

%e   1, 33, 73, 165, 341, 363, 439, 495, 511;

%e   ...

%e (End)

%Y Cf. A038870.

%K nonn,tabf,easy

%O 1,4

%A Francois Maurel (maurel(AT)sequoia.ens.fr)