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Number of distinct non-extendable sequences (x(1),x(2),...,x(k)) such that each x(i) is in {1,2,...,n} and (x(j) AND x(i)) <> x(j) for i=2..k, j=1..i-1.
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%I #10 Jan 04 2022 21:03:14

%S 1,2,4,14,38,126,252,1662,7180,39430,111064,803876,2863992,12123360,

%T 24246720,329012784,2602608516

%N Number of distinct non-extendable sequences (x(1),x(2),...,x(k)) such that each x(i) is in {1,2,...,n} and (x(j) AND x(i)) <> x(j) for i=2..k, j=1..i-1.

%D Related to Mathematical Recreations, Scientific American, March 2000.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a053/A053623.java">Java program</a> (github)

%e a(3)=4, since the allowable sequences are (1,2), (2,1), (3,1,2), (3,2,1).

%e (1,3) is not allowed because 1 AND 3 = 01 AND 11 (base 2) = 1.

%e (3,1) is not allowed because it can be extended to (3,1,2).

%Y Cf. A054668.

%K nonn

%O 1,2

%A _John W. Layman_, Mar 21 2000

%E a(17) from _Sean A. Irvine_, Jan 04 2022