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A095817 Number of permutations of 1..n with no four elements in correct or reverse order. 2
1, 1, 2, 6, 22, 114, 692, 4884, 39318, 355490, 3567292, 39345804, 473148014, 6161310442, 86376341412, 1297099489668, 20772929663254, 353415786538434, 6365693021157116, 121016486728717740, 2421505946364174606, 50873034832373299370, 1119617627206173146308 (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) or (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 = 4. - Ivana Jovovic ( ivana121(AT)EUnet.yu ), Nov 11 2007
PROG
(PARI) seq(n)={my(m=4); 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
Sequence in context: A290279 A014371 A111280 * A370525 A352413 A101042
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 March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)