0,3

Nonoverlapping means that the intervals associated with the minimum to maximum integers of any two blocks of a partition do not overlap. Instead, the intervals are disjoint or one contains another.

Apparently, also the number of permutations in S_n avoiding 2{bar 5}3{bar 1}4 (i.e. every occurrence of 234 is contained in an occurrence of a 25314). - Lara Pudwell (lpudwell(AT)math.rutgers.edu), Apr 25 2008

A. Claesson, Generalized pattern avoidance, Europ. J. Combin., 22 (2001), 961-971.

M. Klazar, Bell numbers, their relatives, and algebraic differential equations, J. Combin. Theory, A 102 (2003), 63-87.

M. Klazar, Bell numbers, their relatives, and algebraic differential equations

A. Claesson and T. Mansour, Permutations avoiding a pair of generalized patterns....

P. Flajolet and R. Schott, Non-overlapping Partitions, Continued Fractions, Bessel Functions and a Divergent Series In European Journal of Combinatorics, Vol. 11, 1990, pp. 412-432.

Index entries for sequences related to Bessel functions or polynomials

G.f. 1/(1-x-x^2/(1-2x-x^2/(1-3x-x^2/...))) (a continued fraction).

(PARI) {a(n)=local(A); if(n<0, 0, A=O(x^0); for(i=0, n\2, A=subst((1+x)/(1-x^2*A), x, x/(1-x))); polcoeff(A, n))} /* Michael Somos Sep 22 2005 */

(PARI) {a(n)=local(m); if(n<0, 0, m=contfracpnqn(matrix(2, n\2, i, k, if(i==1, -x^2, 1-(k+1)*x))); polcoeff(1/(1-x+m[2, 1]/m[1, 1])+x*O(x^n), n))}

Cf. A000110.

Adjacent sequences: A006786 A006787 A006788 this_sequence A006790 A006791 A006792

Sequence in context: A110489 A005425 A035349 this_sequence A098569 A137549 A014327

nonn

njas, Simon Plouffe (plouffe(AT)math.uqam.ca)

Edited by Michael Somos, Oct 06, 2003