A084659 Number of labeled claw-free cubic graphs on 2n nodes (not necessarily connected).

1, 0, 1, 60, 2555, 466200, 62791575, 14536021500, 8381453705625, 3284480337138000, 1942832950684250625, 2143745512307546647500, 1743194710893176557891875, 2022583790860881671548125000

Offset

0,4

Links

R. J. Mathar, Table of n, a(n) for n = 0..26 Nov 26 2018

B. D. McKay, Edgar M. Palmer, Ronald C. Read and Robert W. Robinson. The asymptotic number of claw-free cubic graphs, Discrete Math., 272 (2003), 107-118.

Edgar M. Palmer, Ronald C. Read and Robert W. Robinson. Counting claw-free cubic graphs, SIAM J. Discrete Math. 16 (2002), 65-73.

Formula

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

Maple

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];

Crossrefs

Cf. A057848.

Sequence in context: A058929 A057848 A082670 * A230568 A180373 A264947

Adjacent sequences: A084656 A084657 A084658 * A084660 A084661 A084662

Keyword

nonn

Author

Gordon F. Royle, Jun 02 2003

Status

approved