A005194 Number of balanced symmetric graphs.
1, 2, 4, 6, 10, 22, 38, 102, 182, 574, 1070, 3798, 7286, 28894, 57374, 248502, 506678, 2384254, 5007230, 25247958, 54311126, 292500574, 645652574, 3680048502, 8301671798, 49967727934, 115334270270, 728281984278, 1714641313046, 11341092707614
Offset: 1
Keywords
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- David A. Sheppard, The factorial representation of balanced labelled graphs, Discrete Math. 15 (1976), no. 4, 379-388.
Formula
Let S(n,j) = j! * j^floor((n-2)/2). If n is even, then a(n) = 2 * Sum_{j=1..n/2} S(n,j). If n is odd, and (n-1)/2 is odd, then a(n) = ((n+1)/2)! + 2 * Sum_{j=1,3,5,...,(n-1)/2} S(n, j). Otherwise, n is odd, and (n-1)/2 is even, then a(n) = ((n+1)/2)! + ((n-1)/2)! + 2 * Sum_{j=1,3,5,...,(n-1)/2-1} S(n, j) [From Sheppard paper]. - Sean A. Irvine, Apr 18 2016
Extensions
More terms from Sean A. Irvine, Apr 18 2016