cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

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%I A123545 #7 Nov 22 2020 20:22:36
%S A123545 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,
%T A123545 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,
%U A123545 0,0,0,0,0,0,0,0,0,5,35,136,309,465,505,438,310,188,103,52,23
%N 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).
%D A123545 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
%H A123545 R. W. Robinson, <a href="/A123545/b123545.txt">Rows 1 through 14, flattened</a>
%e A123545 Triangle begins:
%e A123545 n = 1
%e A123545 k = 0 : 0
%e A123545 ************************ TOTAL (n = 1) = 0
%e A123545 n = 2
%e A123545 k = 0 : 0
%e A123545 k = 1 : 0
%e A123545 ************************ TOTAL (n = 2) = 0
%e A123545 n = 3
%e A123545 k = 0 : 0
%e A123545 k = 1 : 0
%e A123545 k = 2 : 0
%e A123545 k = 3 : 0
%e A123545 ************************ TOTAL (n = 3) = 0
%e A123545 n = 4
%e A123545 k = 0 : 0
%e A123545 k = 1 : 0
%e A123545 k = 2 : 0
%e A123545 k = 3 : 0
%e A123545 k = 4 : 0
%e A123545 k = 5 : 0
%e A123545 k = 6 : 1
%e A123545 ************************ TOTAL (n = 4) = 1
%e A123545 n = 5
%e A123545 k = 0 : 0
%e A123545 k = 1 : 0
%e A123545 k = 2 : 0
%e A123545 k = 3 : 0
%e A123545 k = 4 : 0
%e A123545 k = 5 : 0
%e A123545 k = 6 : 0
%e A123545 k = 7 : 0
%e A123545 k = 8 : 1
%e A123545 k = 9 : 1
%e A123545 k = 10 : 1
%e A123545 ************************ TOTAL (n = 5) = 3
%e A123545 From _Hugo Pfoertner_, Nov 22 2020: (Start)
%e A123545 Transposed table:
%e A123545                             Nodes                             Sums
%e A123545        4  5  6   7    8      9      10      11     12    13 |A338604
%e A123545   Edges-----------------------------------------------------|-------
%e A123545    6 | 1  .  .   .    .      .       .       .      .     . |      1
%e A123545    7 | .  .  .   .    .      .       .       .      .     . |      0
%e A123545    8 | .  1  .   .    .      .       .       .      .     . |      1
%e A123545    9 | .  1  2   .    .      .       .       .      .     . |      3
%e A123545   10 | .  1  4   .    .      .       .       .      .     . |      5
%e A123545   11 | .  .  5   4    .      .       .       .      .     . |      9
%e A123545   12 | .  .  4  18    5      .       .       .      .     . |     27
%e A123545   13 | .  .  2  30   35      .       .       .      .     . |     67
%e A123545   14 | .  .  1  34  136     27       .       .      .     . |    198
%e A123545   15 | .  .  1  29  309    288      19       .      .     . |    646
%e A123545   16 | .  .  .  17  465   1377     357       .      .     . |   2216
%e A123545   17 | .  .  .   9  505   3978    3478     208      .     . |   8178
%e A123545   18 | .  .  .   5  438   7956   18653    4958     85     . |  32085
%e A123545   19 | .  .  .   2  310  11904   65011   50575   4291     . | 132093
%e A123545   20 | .  .  .   1  188  14134  163812  302854  85421  1958 | 568368
%e A123545 (End)
%Y A123545 Row sums give A007112. Cf. A123546, A338604.
%K A123545 nonn,tabf
%O A123545 1,35
%A A123545 _N. J. A. Sloane_, Nov 13 2006