A275744 Triangle read by rows: Number of unlabeled cubic graphs with 2n nodes and k components.
0, 1, 0, 2, 0, 0, 5, 1, 0, 0, 19, 2, 0, 0, 0, 85, 8, 1, 0, 0, 0, 509, 29, 2, 0, 0, 0, 0, 4060, 138, 8, 1, 0, 0, 0, 0, 41301, 774, 33, 2, 0, 0, 0, 0, 0, 510489, 5693, 153, 8, 1, 0, 0, 0, 0, 0, 7319447, 53581, 861, 33, 2, 0, 0, 0, 0, 0, 0, 117940535, 626717, 6173, 158, 8, 1
Offset: 1
Examples
The triangle starts
0;
1 0;
2 0 0;
5 1 0 0;
19 2 0 0 0;
85 8 1 0 0 0;
509 29 2 0 0 0 0;
4060 138 8 1 0 0 0 0;
41301 774 33 2 0 0 0 0 0;
.510489 5693 153 8 1 0 0 0 0 0;
...
Crossrefs
Cf. A005638 (row sums).
Formula
T(n,1) = A002851(n).
T(n,k) = Sum_{c_i*N_i=n,i=1..k} binomial(T(N_i,1)+c_i-1,c_i) for 1
G.f.: Product_{j>=1} (1-y*x^j)^(-A002851(j)). - Alois P. Heinz, Apr 13 2017
Comments