

A294522


Triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with diameter k (0<=k<n).


7



1, 0, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 14, 5, 1, 0, 1, 59, 43, 8, 1, 0, 1, 373, 387, 82, 9, 1, 0, 1, 4154, 5797, 1027, 125, 12, 1, 0, 1, 91518, 148229, 19320, 1818, 180, 13, 1, 0, 1, 4116896, 6959721, 598913, 37856, 2928, 239, 16, 1
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OFFSET

1,9


LINKS

Table of n, a(n) for n=1..55.
Eric Weisstein's World of Mathematics, Graph Diameter
Wikipedia, Distance (graph theory)


FORMULA

a(n,1) = 1 for n > 1 (only K_n has diameter 1).
a(n,n1) = 1 (only P_n has diameter n1).


EXAMPLE

Triangle begins:
1;
0, 1;
0, 1, 1;
0, 1, 4, 1;
0, 1, 14, 5, 1;
0, 1, 59, 43, 8, 1;
0, 1, 373, 387, 82, 9, 1;
0, 1, 4154, 5797, 1027, 125, 12, 1;
...
From Eric W. Weisstein, Jun 11 2019: (Start)
a(2,1) = 1 since only P_2 has diameter 1.
a(3,1) = 1 since only C_3 has diameter 1.
a(3,2) = 1 since only P_3 has diameter 2.
a(4,1) = 1 since only K_4 has diameter 1.
a(4,2) = 4 since K_1,3, K4e, the paw graph, and C_4 have diameter 2.
a(4,3) = 1 since only P_4 has diameter 3.
(End)


CROSSREFS

Columns k=0..6 are A000007, A057427, A241706, A241707, A241708, A241709, A241710.
Row sums give A001349.
Sequence in context: A173018 A055105 A200545 * A058710 A281891 A124539
Adjacent sequences: A294519 A294520 A294521 * A294523 A294524 A294525


KEYWORD

nonn,tabl


AUTHOR

Andrew Howroyd, Nov 01 2017


STATUS

approved



