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Search: id:A084659
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| A084659 |
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Number of labeled claw-free cubic graphs on 2n nodes (not necessarily connected). |
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1
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| 1, 0, 1, 60, 2555, 466200, 62791575, 14536021500, 8381453705625, 3284480337138000, 1942832950684250625, 2143745512307546647500, 1743194710893176557891875, 2022583790860881671548125000
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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Edgar M. Palmer, Ronald C. Read and Robert W. Robinson. Counting claw-free cubic graphs, SIAM J. Discrete Math. 16 (2002), 65-73.
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.
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FORMULA
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Recurrence is given in Maple code below. For asymptotics see the 2003 paper.
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MAPLE
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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];
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CROSSREFS
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Cf. A057848.
Sequence in context: A058929 A057848 A082670 this_sequence A004297 A053401 A159991
Adjacent sequences: A084656 A084657 A084658 this_sequence A084660 A084661 A084662
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KEYWORD
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nonn
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AUTHOR
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Gordon Royle (gordon(AT)maths.uwa.edu.au), Jun 02 2003
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