A136283 Number of graphs on n labeled nodes with degree at most 4.

1, 2, 8, 64, 1024, 27449, 1052793, 53470067, 3451287371, 275322712826, 26566919914276, 3047264283807562, 409523561958024458, 63703577287372238069, 11351386036074641226649, 2296295762734645223170899, 523223196906671550193022083, 133357299601279100522308107142

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