A294218 Triangle read by rows: T(n,k) is the number of graphs with n vertices and arboricity k (n >= 1, 1 <= k <= ceiling(n/2)).

1, 2, 3, 1, 6, 5, 10, 22, 2, 20, 114, 22, 37, 703, 300, 4, 76, 5946, 6204, 120, 153, 68505, 198406, 7595, 9, 329, 1042310, 9901453, 1060264, 812

Offset

1,2

Comments

Row sums give A000088(n).

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Arboricity

Formula

T(n,1) = A005195(n).

Example

Triangle begins:
1;
2;
3,1;
6,5;
10,22,2;
20,114,22;
37,703,300,4;
76,5946,6204,120;

Crossrefs

Cf. A000088 (simple graphs on n nodes).

Cf. A005195 (forests on n nodes).

Sequence in context: A076631 A035485 A074306 * A356013 A366139 A347945

Adjacent sequences: A294215 A294216 A294217 * A294219 A294220 A294221

Keyword

nonn,tabf

Author

Eric W. Weisstein, Oct 25 2017

Extensions

Row 10 from Eric W. Weisstein, Nov 21 2017

Status

approved