A300705 Triangle T(n,k) read by rows: the number of n-node connected graphs with k components with no cycles of length less than 5.

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 4, 3, 2, 1, 1, 0, 8, 7, 4, 2, 1, 1, 0, 18, 14, 8, 4, 2, 1, 1, 0, 47, 33, 17, 9, 4, 2, 1, 1, 0, 137, 81, 40, 18, 9, 4, 2, 1, 1, 0, 464, 228, 98, 43, 19, 9, 4, 2, 1, 1, 0, 1793, 716, 269, 105, 44, 19, 9, 4, 2, 1, 1, 0, 8167, 2596, 827, 287, 108, 45, 19, 9, 4, 2, 1, 1, 0

Offset

0,12

Comments

Multiset transform of A126757.

Links

Table of n, a(n) for n=0..91.

Example

The triangle starts in row n=0 with columns 0<=k<=n as:
 1;
0 1
0 1 1
0 1 1 1
0 2 2 1 1
0 4 3 2 1 1
0 8 7 4 2 1 1
0 18 14 8 4 2 1 1
0 47 33 17 9 4 2 1 1
0 137 81 40 18 9 4 2 1 1
0 464 228 98 43 19 9 4 2 1 1
0 1793 716 269 105 44 19 9 4 2 1 1
0 8167 2596 827 287 108 45 19 9 4 2 1 1
0 43645 11030 2904 870 294 109 45 19 9 4 2 1 1
0 275480 55628 11992 3022 888 297 110 45 19 9 4 2 1 1
0 2045279 334676 58968 12320 3066 895 298 110 45 19 9 4 2 1 1
0 17772647 2395216 348166 59991 12440 3084 898 299 110 45 19 9 4 2 1 1

Crossrefs

Cf. A126757 (column k=1), A006787 (row sums)

Sequence in context: A105821 A342936 A004564 * A144157 A321400 A004562

Adjacent sequences: A300702 A300703 A300704 * A300706 A300707 A300708

Keyword

nonn,tabl

Author

R. J. Mathar, Mar 12 2018

Status

approved