The first, 40, terms of the sequence enumerating permutations of length n suc\
    h that pi[i+3]-pi[i] is never 4 are



            or equivalently, such that pi[i+4]-pi[i] is never 3, are

[1, 2, 6, 24, 108, 588, 3768, 28032, 237024, 2252460, 23751072, 274983552, 
3466724112, 47252955456, 692321814144, 10848815656704, 181035316685424, 
3204767043076320, 59981575683074400, 1183379432694727104, 24544072318504622400,
533866158175176897120, 12151412059886415338976, 288842063166373485029184, 
7157123228966286264597792, 184557216285772760437690464, 
4944990987860216238553374720, 137473872218020872340608302784, 
3960212343622024003641964772064, 118065851255846195021860880196960, 
3638629309563846885184822445273856, 115795547778291329977944856503475968, 
3801446422084112421525611126996320128, 128616921438443663423241266743387508640,
4480776208614890038584920347805200701984, 
160601754048375273732337973685245134102656, 
5917599801365546063340453195639552065304384, 
223982606988871416393136444677250082193209568, 
8702594540452708815177045624444277358324332512, 
346862379592138836041844801500892816777938311296]


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