A095818 Number of permutations of 1..n with no five elements in correct or reverse order.

1, 1, 2, 6, 24, 118, 714, 5012, 40164, 361872, 3621366, 39854930, 478427452, 6221137644, 87112280208, 1306869108686, 20912175669082, 355537064658852, 6400095163337508, 121608318630457872, 2432271817858395382, 51079520016325649394, 1123782363517325646716

Offset

0,3

Comments

For no k do either of the subsequences k(k+1)(k+2)(k+3)(k+4) or (k+4)(k+3)(k+2)(k+1)k occur in any permutation.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

D. M. Jackson and R. C. Read, A note on permutations without runs of given length, Aequationes Math. 17 (1978), no. 2-3, 336-343.

Formula

G.f.: Sum_{n>=0} n!*((2*x^m-x^(m+1)-x)/(x^m-1))^n where m = 5. - Ivana Jovovic ( ivana121(AT)EUnet.yu ), Nov 11 2007

Prog

(PARI) seq(n)={my(m=5); Vec(sum(k=0, n, k!*((2*x^m-x^(m+1)-x)/(x^m-1) + O(x*x^n))^k))} \\ Andrew Howroyd, Aug 31 2018

Crossrefs

Cf. A002464, A095816, A095817.

Sequence in context: A135106 A248837 A005394 * A369098 A264781 A224316

Adjacent sequences: A095815 A095816 A095817 * A095819 A095820 A095821

Keyword

nonn

Author

Jonas Wallgren, Jun 08 2004

Extensions

More terms from Ivana Jovovic ( ivana121(AT)EUnet.yu ), Nov 11 2007

a(0)=1 prepended and terms a(20) and beyond from Andrew Howroyd, Aug 31 2018

Status

approved