A085584 Number of (3412,2341)-, (3412,4123)- and (3412,52341)-avoiding involutions in S_n.

1, 2, 4, 9, 20, 45, 100, 222, 491, 1086, 2401, 5310, 11744, 25977, 57460, 127101, 281144, 621882, 1375579, 3042726, 6730385, 14887338, 32930188, 72840249, 161119700, 356390301, 788321020, 1743734406, 3857070395, 8531684622

Offset

1,2

Links

Table of n, a(n) for n=1..30.

E. S. Egge, Restricted 3412-Avoiding Involutions: Continued Fractions, Chebyshev Polynomials and Enumerations, sec. 8

Formula

G.f. (1-x^2)*(1-x)^2/(1-3*x+x^2+3*x^3-3*x^4).

Mathematica

CoefficientList[Series[(1-x^2)(1-x)^2/(1-3x+x^2+3x^3-3x^4), {x, 0, 40}], x] (* Harvey P. Dale, May 28 2017 *)

Crossrefs

Sequence in context: A144686 A108469 A144685 * A369614 A080019 A052534

Adjacent sequences: A085581 A085582 A085583 * A085585 A085586 A085587

Keyword

nonn,easy

Author

Ralf Stephan, Jul 06 2003

Status

approved