A294223 Triangle read by rows: T(n,k) is the number of graphs with n vertices and bandwidth k.

1, 2, 3, 1, 5, 5, 1, 7, 18, 8, 1, 11, 60, 70, 14, 1, 15, 195, 580, 233, 20, 1, 22, 623, 4942, 5902, 826, 30, 1, 30, 1989, 41332, 165514, 62562, 3196, 44, 1

Offset

1,2

Comments

a(1) = T(1,1) uses the convention that the bandwidth of the singleton graph is 1.

Row 1 is of length 1; row n if of length n-1 for n > 1.

Row sums give A000088(n).

Links

Table of n, a(n) for n=1..37.

Eric Weisstein's World of Mathematics, Graph Bandwidth

Formula

T(n,1) = A000041(n).

T(n,n-1) = 1 for n > 2.

Example

Triangle begins:
1
2
3,1
5,5,1
7,18,8,1
11,60,70,14,1
15,195,580,233,20,1
22,623,4942,5902,826,30,1

Crossrefs

Cf. A000088 (number of simple graphs on n nodes).

Cf. A000041 (number of partitions of n).

Sequence in context: A345145 A114690 A336364 * A355618 A238122 A214059

Adjacent sequences: A294220 A294221 A294222 * A294224 A294225 A294226

Keyword

nonn,tabf,more

Author

Eric W. Weisstein, Oct 25 2017

Status

approved