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A123545 Triangle read by rows: T(n,k) = number of unlabeled connected graphs on n nodes with degree >= 3 at each node (n >= 1, 0 <= k <= n(n-1)/2). 9
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 5, 4, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 18, 30, 34, 29, 17, 9, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 35, 136, 309, 465, 505, 438, 310, 188, 103, 52, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,35

REFERENCES

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.

LINKS

R. W. Robinson, Rows 1 through 14, flattened

EXAMPLE

Triangle begins:

n = 1

k = 0 : 0

************************ TOTAL (n = 1) = 0

n = 2

k = 0 : 0

k = 1 : 0

************************ TOTAL (n = 2) = 0

n = 3

k = 0 : 0

k = 1 : 0

k = 2 : 0

k = 3 : 0

************************ TOTAL (n = 3) = 0

n = 4

k = 0 : 0

k = 1 : 0

k = 2 : 0

k = 3 : 0

k = 4 : 0

k = 5 : 0

k = 6 : 1

************************ TOTAL (n = 4) = 1

n = 5

k = 0 : 0

k = 1 : 0

k = 2 : 0

k = 3 : 0

k = 4 : 0

k = 5 : 0

k = 6 : 0

k = 7 : 0

k = 8 : 1

k = 9 : 1

k = 10 : 1

************************ TOTAL (n = 5) = 3

From Hugo Pfoertner, Nov 22 2020: (Start)

Transposed table:

Nodes Sums

4 5 6 7 8 9 10 11 12 13 |A338604

Edges-----------------------------------------------------|-------

6 | 1 . . . . . . . . . | 1

7 | . . . . . . . . . . | 0

8 | . 1 . . . . . . . . | 1

9 | . 1 2 . . . . . . . | 3

10 | . 1 4 . . . . . . . | 5

11 | . . 5 4 . . . . . . | 9

12 | . . 4 18 5 . . . . . | 27

13 | . . 2 30 35 . . . . . | 67

14 | . . 1 34 136 27 . . . . | 198

15 | . . 1 29 309 288 19 . . . | 646

16 | . . . 17 465 1377 357 . . . | 2216

17 | . . . 9 505 3978 3478 208 . . | 8178

18 | . . . 5 438 7956 18653 4958 85 . | 32085

19 | . . . 2 310 11904 65011 50575 4291 . | 132093

20 | . . . 1 188 14134 163812 302854 85421 1958 | 568368

(End)

CROSSREFS

Row sums give A007112. Cf. A123546, A338604.

Sequence in context: A266408 A230564 A011174 * A123546 A339069 A334422

Adjacent sequences: A123542 A123543 A123544 * A123546 A123547 A123548

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Nov 13 2006

STATUS

approved

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)