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A095818 Number of permutations of 1..n with no five elements in correct or reverse order. 3
1, 1, 2, 6, 24, 118, 714, 5012, 40164, 361872, 3621366, 39854930, 478427452, 6221137644, 87112280208, 1306869108686, 20912175669082, 355537064658852, 6400095163337508, 121608318630457872, 2432271817858395382, 51079520016325649394, 1123782363517325646716 (list; graph; refs; listen; history; text; internal format)
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 * A264781 A224316 A256195

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

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Last modified January 27 21:49 EST 2023. Contains 359849 sequences. (Running on oeis4.)