A275420 Triangle read by rows: T(n,k) = number of graphs with n nodes and k connected regular components.

1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 5, 5, 4, 2, 1, 1, 4, 9, 6, 4, 2, 1, 1, 17, 14, 12, 7, 4, 2, 1, 1, 22, 30, 19, 13, 7, 4, 2, 1, 1, 167, 56, 42, 22, 14, 7, 4, 2, 1, 1, 539, 224, 74, 47, 23, 14, 7, 4, 2, 1, 1, 18979, 785, 271, 87, 50, 24, 14, 7, 4, 2, 1, 1, 389436, 19783

Offset

1,7

Comments

Multiset transformation of A005177.

The resulting graph has each component regular but may not be regular itself since different components can have different degrees. - Andrew Howroyd, May 20 2020

Links

Andrew Howroyd, Table of n, a(n) for n = 1..300 (rows 1..24)

Index entries for triangles generated by the Multiset Transformation

Formula

T(n,1) = A005177(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)^(-A005177(j)). - Alois P. Heinz, Apr 13 2017

Example

      1
      1   1
      1   1   1
      2   2   1   1
      2   3   2   1   1
      5   5   4   2   1   1
      4   9   6   4   2   1   1
     17  14  12   7   4   2   1   1
     22  30  19  13   7   4   2   1   1
    167  56  42  22  14   7   4   2   1   1
    539 224  74  47  23  14   7   4   2   1   1
  18979 785 271  87  50  24  14   7   4   2   1   1

Crossrefs

Cf. A005177 (1st column), A165647 (row sums).

Sequence in context: A011847 A091325 A193596 * A344961 A343853 A143974

Adjacent sequences: A275417 A275418 A275419 * A275421 A275422 A275423

Keyword

nonn,tabl

Author

R. J. Mathar, Jul 27 2016

Extensions

Name clarified by Andrew Howroyd, May 20 2020

Status

approved