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A256335 Number of Largest Chain Family matchings on n edges. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

REFERENCES

A. Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, Ph. D. Dissertation, Univ. of Florida, Math., 2015.

LINKS

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

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: A193661 A192296 A002893 * A258313 A074539 A103210

Adjacent sequences:  A256332 A256333 A256334 * A256336 A256337 A256338

KEYWORD

nonn

AUTHOR

Aziza Jefferson, Mar 25 2015

STATUS

approved

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Last modified April 19 22:22 EDT 2019. Contains 322291 sequences. (Running on oeis4.)