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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
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
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
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