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A092807 Expansion of (1-6*x+4*x^2)/((1-2*x)*(1-6*x)). 0
1, 2, 8, 40, 224, 1312, 7808, 46720, 280064, 1679872, 10078208, 60467200, 362799104, 2176786432, 13060702208, 78364180480, 470185017344, 2821109972992, 16926659575808, 101559956930560, 609359740534784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Second binomial transform of A054881 (closed walks at a vertex of an octahedron) With interpolated zeros, counts closed walks of length n at a vertex of the edge-vertex incidence graph of K_4 associated with the edges of K_4.

This also gives the number of noncrossing, nonnesting, 2-colored permutations on {1, 2, ..., n}. - Lily Yen, Apr 22 2013

LINKS

Table of n, a(n) for n=0..20.

Lily Yen, Crossings and Nestings for Arc-Coloured Permutations, arXiv:1211.3472 [math.CO], 2012-2013 and Arc-coloured permutations, PSAC 2013, Paris, France, June 24-28, Proc. DMTCS (2013) 743-754

Lily Yen, Crossings and Nestings for Arc-Coloured Permutations and Automation, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.

Index entries for linear recurrences with constant coefficients, signature (8,-12).

FORMULA

a(n) = 6^n/6+2^n/2+0^n/3

a(n) = A074601(n-1), n>0. [R. J. Mathar, Sep 08 2008]

a(0)=1, a(1)=2, a(2)=8, a(n) = 8*a(n-1)-12*a(n-2). [Harvey P. Dale, Aug 23 2011]

a(n) = A124302(n)*2^n. - Philippe Deléham, Nov 01 2011

MATHEMATICA

CoefficientList[Series[(1-6x+4x^2)/((1-2x)(1-6x)), {x, 0, 40}], x] (* or *) Join[{1}, LinearRecurrence[{8, -12}, {2, 8}, 40]] (* Harvey P. Dale, Aug 23 2011 *)

CROSSREFS

Cf. A092803.

Sequence in context: A006195 A214763 A219587 * A074601 A214760 A052701

Adjacent sequences:  A092804 A092805 A092806 * A092808 A092809 A092810

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 06 2004

STATUS

approved

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Last modified November 27 16:20 EST 2021. Contains 349394 sequences. (Running on oeis4.)