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



[1, 2, 6, 24, 114, 628, 4062, 30360, 255186, 2414292, 25350954, 292378968,

    3673917102, 49928069188, 729534877758, 11403682481112, 189862332575658,

    3354017704180052, 62654508729565554, 1233924707891272728,

    25550498290562247438, 554913370184289495780, 12612648556263898345758,

    299411750583810718488216, 7409924986737790240296258,

    190856850583975937020030228, 5108283222440036893650974970,

    141870112250977140975169694808, 4082973503947066134710463043374,

    121616802487841972048586204012740, 3744899397363811580125047321071934,

    119082343961934371268047348260787928, 3906394323729047896372054813609731738,

    132073019281315044040357960799728514580,

    4598051703085723629021521115097009617090,

    164698684622791948865479761971150102229528,

    6064825145177982610574856236858905067695950,

    229420634696668968001790413123421777141042404,

    8908902242217781803662578524801135304840564830,

    354895821406788171643098383643659158922659803288]



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