|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
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
|
|
|
|