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

1,4

Comments

Multiset transformation of A002851.

Links

Table of n, a(n) for n=1..72.

Index entries for triangles generated by the Multiset Transformation

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<k<=n.

G.f.: Product_{j>=1} (1-y*x^j)^(-A002851(j)). - Alois P. Heinz, Apr 13 2017

Example

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).

Sequence in context: A094597 A202992 A158830 * A290321 A145430 A143160

Adjacent sequences: A275741 A275742 A275743 * A275745 A275746 A275747

Keyword

nonn,tabl

Author

R. J. Mathar, Aug 07 2016

Status

approved