A259971
Triangle read by rows: coefficients xi(n,k) arising from the study of completely transitive graphs on n nodes.
Original entry on oeis.org
1, 1, 1, 2, 5, 3, 10, 40, 51, 21, 122, 644, 1236, 1029, 315, 3346, 21496, 54060, 66780, 40635, 9765, 196082, 1471460, 4527228, 7328580, 6596100, 3134565, 615195
Offset: 1
Triangle begins:
1,
1,1,
2,5,3,
10,40,51,21,
122,644,1236,1029,315,
3346,21496,54060,66780,40635,9765,
196082,1471460,4527228,7328580,6596100,3134565,615195,
...
- E. Andresen, K. Kjeldsen, On certain subgraphs of a complete transitively directed graph, Discrete Math. 14 (1976), no. 2, 103-119.
- Hsien-Kuei Hwang, Emma Yu Jin, Michael J. Schlosser, Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow, arXiv:2012.13570 [math.CO], Dec 25 2020, p. 29.
A005332
Certain subgraphs of a directed graph.
Original entry on oeis.org
1, 7, 58, 838, 25171, 1610977, 214838128, 58540023808, 32208188445841, 35543124039418147, 78391002506394742198, 344921660620756227029578, 3025372940760065880037836511, 52886001393832278158415800800117, 1842588406743140390123203185385824268, 127974225758895121562137768141145597226148
Offset: 2
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
-
p[n_]:=Product[2^k-1, {k,n}]; a[n_]:=Sum[(Binomial[n-1, i] * p[n-1-i] * 2^i*Sum [(-1)^j*(n-1-i-j)/p[j], {j,0,n-2-i}] ), {i,0,n-2}]; Table[a[n], {n,2,17}] (* Stefano Spezia, Sep 07 2022 *)
-
p(n) = prod(k=1, n, 2^k-1);
a(n) = sum(i=0, n-2, binomial(n-1, i) * p(n-1-i) * 2^i * sum(j=0, n-2-i, (-1)^j * (n-1-i-j) / p(j))); \\ Michel Marcus, May 10 2016
Showing 1-2 of 2 results.