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A136283 Number of graphs on n labeled nodes with degree at most 4. 4
1, 2, 8, 64, 1024, 27449, 1052793, 53470067, 3451287371, 275322712826, 26566919914276, 3047264283807562, 409523561958024458, 63703577287372238069, 11351386036074641226649, 2296295762734645223170899, 523223196906671550193022083, 133357299601279100522308107142 (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

Andrew Howroyd, Table of n, a(n) for n = 1..50

PROG

(PARI)

GraphsWithDegreeAtMost(n, limit)={

local(M=Map());

my(acc(p, v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v)));

my(recurse(p, i, q, v, e)=if(e<=limit&&poldegree(q)<=limit, if(i<0, acc(x^e+q, v), my(t=polcoeff(p, i)); for(k=0, t, self()(p, i-1, (t-k+x*k)*x^i+q, binomial(t, k)*v, e+k)))));

my(iterate(v, k, f)=for(i=1, k, v=f(v)); v);

vecsum(Vec(iterate(Mat([1, 1]), n-1, src->M=Map(); for(i=1, matsize(src)[1], my(p=src[i, 1]); recurse(p, poldegree(p), 0, src[i, 2], 0)); Mat(M)))[2]); }

a(n) = GraphsWithDegreeAtMost(n, 4); \\ Andrew Howroyd, Aug 25 2017

CROSSREFS

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

Sequence in context: A178169 A191572 A191573 * A139680 A153544 A153572

Adjacent sequences:  A136280 A136281 A136282 * A136284 A136285 A136286

KEYWORD

nonn

AUTHOR

Don Knuth, Mar 31 2008

EXTENSIONS

Terms a(13) and beyond from Andrew Howroyd, Aug 25 2017

STATUS

approved

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Last modified September 25 22:57 EDT 2018. Contains 315425 sequences. (Running on oeis4.)