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%I #4 Jul 09 2016 17:34:53
%S 1,1,2,4,8,16,32,68,144,304,692,1580,3602,8976,22552,56850,157740,
%T 442101,1249124,3868420,12082568,38117838,130394944,448733361,
%U 1559590892,5817284716,21787658638,82365982741,331668252301,1339477442569,5457855667219,23555837192320
%N Number of set partitions of [n] such that the difference between each element and its index (in the partition) is a multiple of three.
%e a(7) = 68: 1234567, 123456|7, 12345|67, 12345|6|7, 1234|567, 1234|56|7, 1234|5|67, 1234|5|6|7, 123|4567, 123|456|7, 123|45|67, 123|45|6|7, 123|4|567, 123|4|56|7, 123|4|5|67, 123|4|5|6|7, 12|34567, 12|3456|7, 12|345|67, 12|345|6|7, 12|34|567, 12|34|56|7, 12|34|5|67, 12|34|5|6|7, 12|3|4567, 12|3|456|7, 12|3|45|67, 12|3|45|6|7, 12|3|4|567, 12|3|4|56|7, 12|3|4|5|67, 12|3|4|5|6|7, 1567|234, 1|234567, 1|23456|7, 1|2345|67, 1|2345|6|7, 1|234|567, 1|234|56|7, 1|234|5|67, 1|234|5|6|7, 1567|23|4, 1|23|4567, 1|23|456|7, 1|23|45|67, 1|23|45|6|7, 1|23|4|567, 1|23|4|56|7, 1|23|4|5|67, 1|23|4|5|6|7, 1567|2|34, 1|2|34567, 1|2|3456|7, 1|2|345|67, 1|2|345|6|7, 1|2|34|567, 1|2|34|56|7, 1|2|34|5|67, 1|2|34|5|6|7, 1567|2|3|4, 1|2|3|4567, 1|2|3|456|7, 1|2|3|45|67, 1|2|3|45|6|7, 1|2|3|4|567, 1|2|3|4|56|7, 1|2|3|4|5|67, 1|2|3|4|5|6|7.
%Y Column k=3 of A274859.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jul 09 2016