The first, 40, terms of the sequence enumerating permutations of length n suc\
    h that pi[i+2]-pi[i] is never 4 are



            or equivalently, such that pi[i+4]-pi[i] is never 2 are

[1, 2, 6, 24, 102, 544, 3480, 25944, 220308, 2103280, 22267464, 258731736, 
3272134452, 44730567808, 657118903128, 10322461311000, 172640373779220, 
3062488841908432, 57428041336168488, 1134996967159452312, 23578970729098529364,
513649562721606586720, 11707696306745481688152, 278659373809358532000984, 
6913254482346326278969428, 178472672513539944721144624, 
4787091918527589331581205320, 133218232423238577803066798424, 
3841256747999729575774795026228, 114621696869863289989638111958720, 
3535462778557195348669757699383704, 112602037234219748433581049305868696, 
3699395519170581012617058814997058132, 125253680563408568997302976350830463248,
4366569698246206370774711148480089406888, 
156609318261518653524946795441774634639640, 
5774036664647278639517932157386144259381460, 
218676583726728825714366041014439281192115872, 
8501176735585197320086009417079962899770294808, 
339014958761616274028609971207648002296075746392]


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                         This took, 2665.746, seconds.