A256335 Number of Largest Chain Family matchings on n edges.

1, 3, 15, 93, 639, 4670, 35607, 280069, 2255979, 18516875, 154313881, 1302252294, 11106135906, 95571461319, 828803505465, 7235996887013, 63549647848195, 561049960940540, 4976419846070007, 44325237810194705, 396301576614077927, 3555397444230816343, 31996727212476905751, 288776859922595203094, 2613107152879937592054, 23702850369539462227046, 215483061767106353850246, 1963017891713523908516093, 17917224620763719834090179, 163830901587493323034301583, 1500542646711279198177939831, 13765184019931774406496702885

Offset

1,2

Comments

The Largest Chain Family of matchings is the largest family of matchings formed by repeated edge inflations and vertex insertions into any length n chain.

Links

Table of n, a(n) for n=1..32.

Aziza Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, PhD Thesis, University of Florida, 2015.

Formula

G.f. f satisfies x^3f^6+x^2f^5-4x^2f^4+2xf^3+(x+4)f^2-11f+7 = 0.

Example

a(4)=93 because of the 105 matchings on 4 edges, there are 13 matchings which do not lie in the Largest Chain Family. Two such matching in canonical sequence form, are given by 12343142 and 12342413.

Maple

f := RootOf(_Z^6*x^3+_Z^5*x^2-4*_Z^4*x^2+2*_Z^3*x+_Z^2*x+4*_Z^2-11*_Z+7, 1);
series(f, x=0, 30);

Crossrefs

Sequence in context: A192296 A370218 A002893 * A258313 A368966 A074539

Adjacent sequences: A256332 A256333 A256334 * A256336 A256337 A256338

Keyword

nonn

Author

Aziza Jefferson, Mar 25 2015

Status

approved