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A289444
Irregular triangle read by rows: row n gives the multiplicities of the eigenvalues of the tree graph of the hammock graph P(n+1,2), in order from smallest to largest eigenvalue.
0
3, 1, 6, 2, 3, 1, 10, 8, 9, 4, 1, 15, 20, 25, 4, 10, 5, 1, 21, 40, 60, 24, 25, 15, 6, 1, 28, 70, 126, 84, 70, 6, 35, 21, 7, 1, 36, 112, 238, 224, 196, 48, 77, 56, 28, 8, 1, 45, 168, 414, 504, 504, 216, 189, 8, 126, 84, 36, 9, 1, 55, 240, 675, 1008, 1170, 720, 525, 80, 261, 210, 120, 45, 10, 1
OFFSET
2,1
LINKS
James R. Mahoney, Tree Graphs and Orthogonal Spanning Tree Decompositions, PhD Dissertation, Portland State Univ., 2016.
EXAMPLE
Triangle begins:
3,1,
6,2,3,1,
10,8,9,4,1,
15,20,25,4,10,5,1,
21,40,60,24,25,15,6,1,
28,70,126,84,70,6,35,21,7,1,
36,112,238,224,196,48,77,56,28,8,1,
45,168,414,504,504,216,189,8,126,84,36,9,1,
55,240,675,1008,1170,720,525,80,261,210,120,45,10,1,
...
CROSSREFS
Sequence in context: A158823 A184168 A122913 * A069115 A065275 A071045
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jul 07 2017
STATUS
approved