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Number of labeled claw-free cubic graphs on 2n nodes (not necessarily connected).
1

%I #12 Jan 11 2019 09:28:07

%S 1,0,1,60,2555,466200,62791575,14536021500,8381453705625,

%T 3284480337138000,1942832950684250625,2143745512307546647500,

%U 1743194710893176557891875,2022583790860881671548125000

%N Number of labeled claw-free cubic graphs on 2n nodes (not necessarily connected).

%H R. J. Mathar, <a href="/A084659/b084659.txt">Table of n, a(n) for n = 0..26</a> Nov 26 2018

%H B. D. McKay, Edgar M. Palmer, Ronald C. Read and Robert W. Robinson. <a href="https://dx.doi.org/10.1016/S0012-365X(03)00188-2">The asymptotic number of claw-free cubic graphs</a>, Discrete Math., 272 (2003), 107-118.

%H Edgar M. Palmer, Ronald C. Read and Robert W. Robinson. <a href="http://cobweb.cs.uga.edu/~rwr/publications/claw.pdf">Counting claw-free cubic graphs</a>, SIAM J. Discrete Math. 16 (2002), 65-73.

%F Recurrence is given in Maple code below. For asymptotics see the 2003 paper.

%p cfc[0] := 1; cfc[1] := 0; cfc[n+1] := (6*n-5)*binomial(2*n+1,3)*cfc[n-1] + 60*(2*n^2-7)*binomial(2*n+1,5)*cfc[n-2] + 420*(12*n-31)*binomial(2*n+1,7)*cfc[n-3] - 60480*(4*n-19)*binomial(2*n+1,9)*cfc[n-4] - 3326400*(6*n^2-54*n+127)*binomial(2*n+1,11)*cfc[n-5] - 172972800*(9*n^2-108*n+347)*binomial(2*n+1,13)*cfc[n-6] - 54486432000*(n-1)*binomial(2*n+1,15)*cfc[n-7] + 59281238016000*(n-7)*binomial(2*n+1,17)*cfc[n-8] + 422378820864000*(18*n-97)*binomial(2*n+1,19)*cfc[n-9] + 6563766876226560000*binomial(2*n+1,21)*cfc[n-10] + 673229602575129600000*binomial(2*n+1,23)*cfc[n-11];

%Y Cf. A057848.

%K nonn

%O 0,4

%A _Gordon F. Royle_, Jun 02 2003