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Number of integer n-tuples {x(1),x(2),...,x(n)} with the following properties: (1) x(1)=1 and, for k>1, if d=x(k)-x(k-1), then (2) d is relatively prime to x(k-1) and (3) d=x(i) for some i in {1,2,...,k-1}.
1

%I #12 Jan 03 2024 06:30:35

%S 1,1,1,2,5,17,67,324,1777,11054,76793,591905,4987228,45712331,

%T 452511382,4812134735

%N Number of integer n-tuples {x(1),x(2),...,x(n)} with the following properties: (1) x(1)=1 and, for k>1, if d=x(k)-x(k-1), then (2) d is relatively prime to x(k-1) and (3) d=x(i) for some i in {1,2,...,k-1}.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a054/A054769.java">Java program</a> (github)

%K nonn,more

%O 1,4

%A _John W. Layman_, May 18 2000

%E a(13)-a(16) from _Sean A. Irvine_, Feb 23 2022