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A123474 Triangle read by rows: T(n,k) = number of labeled bicolored nonseparable graphs with k points in one color class and n-k points in the other class. The classes are interchangeable if k = n-k. Here n >= 2, k=1..n-1. 3
1, 0, 0, 0, 3, 0, 0, 10, 10, 0, 0, 15, 340, 15, 0, 0, 21, 6965, 6965, 21, 0, 0, 28, 51296, 246295, 51296, 28, 0, 0, 36, 326676, 14750946, 14750946, 326676, 36, 0, 0, 45, 1917840, 322476210, 796058676, 322476210, 1917840, 45, 0, 0, 55, 10683255 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
2,5
REFERENCES
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..1276 (first 50 rows; first 24 rows from R. W. Robinson)
F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 31 (1979), 60-68.
FORMULA
From Andrew Howroyd, Jan 03 2021: (Start)
T(n,k) = f(n-2*k) * binomial(n,k) * A123301(n, k) where f(0) = 1/2 and 1 otherwise.
A004100(n) = Sum_{k=0..floor(n/2)} T(n,k). (End)
EXAMPLE
Triangle begins:
1;
0, 0;
0, 3, 0;
0, 10, 10, 0;
0, 15, 340, 15, 0;
0, 21, 6965, 6965, 21, 0;
0, 28, 51296, 246295, 51296, 28, 0;
...
Formatted as an array:
==========================================================
m/n | 1 2 3 4 5 6
----+-----------------------------------------------------
1 | 1 0 0 0 0 0 ...
2 | 0 3 10 15 21 28 ...
3 | 0 10 340 6965 51296 326676 ...
4 | 0 15 6965 246295 14750946 322476210 ...
5 | 0 21 51296 14750946 796058676 105725374062 ...
6 | 0 28 326676 322476210 105725374062 9736032295374 ...
...
CROSSREFS
Central coefficients are A005335.
Sequence in context: A244127 A363407 A342312 * A370064 A363033 A321711
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Nov 12 2006
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)