A248426 Number of permutations of length n avoiding the pattern 1342 and with 1 appearing before n.

1, 3, 11, 46, 211, 1038, 5400, 29425, 166767, 977637, 5901299, 36538483, 231286924, 1492482109, 9793849702, 65217085321, 439887071563, 3000650380603, 20673092451143, 143687057466690, 1006538694994567, 7100409431126274, 50404258628152846, 359845398688215262

Offset

2,2

Links

Table of n, a(n) for n=2..25.

Formula

G.f.: (-1 + sqrt((8*x-1)*sqrt(1-8*x) - 136*x^2 + 20*x + 1)/sqrt((8*x-1)*sqrt(1-8*x) - 8*x^2 + 20*x + 1))*((8*x-1)*sqrt(1-8*x) - 8*x^2 - 12*x + 1)/(64*x).

Example

For n=4 the 11 permutations are: 1234, 1243, 1324, 1423, 1432, 2134, 2143, 2314, 3124, 3142, 3214.

Crossrefs

Cf. A022558.

Sequence in context: A086521 A225293 A046996 * A337913 A129579 A030814

Adjacent sequences: A248423 A248424 A248425 * A248427 A248428 A248429

Keyword

nonn

Author

Nathaniel Shar, Oct 06 2014

Status

approved