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A290428 Array read by antidiagonals: T(n,k) is the number of graphs with n edges and k vertices, allowing loops and multi-edges. 4
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 4, 1, 0, 1, 2, 6, 6, 1, 0, 1, 2, 7, 14, 9, 1, 0, 1, 2, 7, 20, 28, 12, 1, 0, 1, 2, 7, 22, 53, 52, 16, 1, 0, 1, 2, 7, 23, 69, 125, 93, 20, 1, 0, 1, 2, 7, 23, 76, 198, 287, 152, 25, 1, 0, 1, 2, 7, 23, 78, 245, 550, 606, 242 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Variant of A138107, here for non-directed edges.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1325

R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 (2017), Table 59

EXAMPLE

1   1   1   1    1    1    1   1   1...

0   1   2   2    2    2    2   2   2...

0   1   4   6    7    7    7   7   7...

0   1   6  14   20   22   23  23  23...

0   1   9  28   53   69   76  78  79...

0   1  12  52  125  198  245 264 271...

0   1  16  93  287  550  782 915 973...

0   1  20 152  606 1441 2392

0   1  25 242 1226 3611

PROG

(PARI)

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^g )) * prod(i=1, #v, my(c=v[i]); t(c)^((c+1)\2)*if(c%2, 1, t(c/2)))}

T(m, n=m) = {Mat(vector(n+1, n, my(s=O(x*x^m)); forpart(p=n-1, s+=permcount(p)*1/edges(p, i->1-x^i+O(x*x^m))); Col(s/(n-1)!)))}

{ my(A=T(8)); for(n=1, #A, print(A[n, ])) } \\ Andrew Howroyd, Oct 22 2019

CROSSREFS

Cf. A050531 (column 3), A050532 (column 4), A138107, A098568 (vertex-labeled).

Sequence in context: A022958 A023444 A248157 * A136868 A276066 A145895

Adjacent sequences:  A290425 A290426 A290427 * A290429 A290430 A290431

KEYWORD

nonn,tabl

AUTHOR

R. J. Mathar, Jul 31 2017

STATUS

approved

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Last modified February 23 12:38 EST 2020. Contains 332159 sequences. (Running on oeis4.)