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A136282 Number of graphs on n labeled nodes with degree at most 3. 5
1, 2, 8, 64, 768, 12068, 236926, 5651384, 160054952, 5284391984, 200375581984, 8620342917808, 416471882713712, 22400989824444576, 1331457489258580672, 86887134810544955072, 6189888588922841477824, 478992737680928902742656, 40082045451011806706919808, 3612470757307682016196841216, 349398857659776033845292636416 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200

FORMULA

Binomial transform of A110041. - Vladeta Jovovic, May 20 2008

Conjecture: 12*(81*n^4 - 837*n^3 + 3375*n^2 - 6171*n + 4192)*a(n) = 6*(243*n^5 - 2511*n^4 + 10665*n^3 - 21969*n^2 + 19476*n - 4624)*a(n-1) + 3*(n-1)*(243*n^6 - 2997*n^5 + 15147*n^4 - 39843*n^3 + 57594*n^2 - 41832*n + 10888)*a(n-2) - 3*(n-2)*(n-1)*(405*n^5 - 3699*n^4 + 13527*n^3 - 22629*n^2 + 14048*n + 388)*a(n-3) + (n-3)*(n-2)*(n-1)*(243*n^5 - 1944*n^4 + 6777*n^3 - 9738*n^2 - 2370*n + 10732)*a(n-4) + 2*(n-4)*(n-3)*(n-2)*(n-1)*(81*n^4 - 999*n^3 + 4968*n^2 - 8646*n + 4906)*a(n-5) + (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(243*n^5 - 2916*n^4 + 12933*n^3 - 27990*n^2 + 27978*n - 8948)*a(n-6) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(81*n^4 - 513*n^3 + 891*n^2 - 357*n - 242)*a(n-7) - (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(81*n^4 - 513*n^3 + 1350*n^2 - 1608*n + 640)*a(n-8). - Vaclav Kotesovec, Aug 13 2013

CROSSREFS

Cf. A000085 (degree at most 1), A136281-A136286.

Sequence in context: A268666 A193549 A005612 * A092934 A224801 A191571

Adjacent sequences:  A136279 A136280 A136281 * A136283 A136284 A136285

KEYWORD

nonn

AUTHOR

Don Knuth, Mar 31 2008

EXTENSIONS

More terms from Vladeta Jovovic, May 20 2008

STATUS

approved

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Last modified September 20 12:42 EDT 2018. Contains 315239 sequences. (Running on oeis4.)