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.

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

Table of n, a(n) for n=2..75.

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

Adjacent sequences: A289441 A289442 A289443 * A289445 A289446 A289447

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jul 07 2017

Status

approved