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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 (list; table; graph; refs; listen; history; text; internal format)
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,n-1) = 1 (only P_n has diameter n-1).

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, K4-e, 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

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Last modified November 21 22:16 EST 2019. Contains 329383 sequences. (Running on oeis4.)