[seqfan] Re: A046718, one 132 and two 123 patterns in [n]

[Heinz, Alois]

I get by brute force counting: 1, 4, 14, 47, 152, ...

a(4)=1: 1324
a(5)=4: 24315, 24351, 41325, 51324
a(6)=14: 354216, 354261, 354612, 354621, 435162, 462135,
524316, 524361, 541326, 561324, 624315, 624351, 641325, 651324
a(7)=47: 4653217, 4653271, 4653712, 4653721, 4657213, 4657231,
4657312, 4657321, 5462713, 5462731, 5463172, 5467132, 5634172,
5637124, 5732416, 5732461, 5734126, 5742136, 5762134, 6354217,
6354271, 6354712, 6354721, 6435172, 6472135, 6524317, 6524371,
6541327, 6571324, 6724315, 6724351, 6741325, 6751324, 7354216,
7354261, 7354612, 7354621, 7435162, 7462135, 7524316, 7524361,
7541326, 7561324, 7624315, 7624351, 7641325, 7651324

So the terms seem to be correct and the g.f. should be

(1-4*x+6*x^2-x^3+7216*x^7-38528*x^8+69504*x^9-42240*x^10)*x^4/(2*x-1)^4

Alois