A209034 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.
4, 33, 144, 471, 1237, 2798, 5648, 10483, 18174, 29863, 46918, 71037, 104183, 148732, 207352, 283199, 379766, 501099, 651612, 836369, 1060813, 1331122, 1653894, 2036531, 2486878, 3013693, 3626176, 4334533, 5149447, 6082684, 7146500, 8354355
Offset: 1
Keywords
Examples
Some solutions for n=6: -4 -2 -4 -5 -4 -3 -1 -2 -3 -2 -3 -4 -4 -6 -3 -3 -2 -2 -2 -1 -1 1 -1 -1 0 -2 -2 -2 -3 0 -2 -2 3 0 1 2 2 0 2 0 -1 -1 -2 -1 1 -1 4 1 1 -2 4 1 -2 0 -1 3 3 1 1 4 5 1 0 4 0 4 -1 2 4 0 -1 -2 0 1 3 1 0 6 -1 2 2 2 2 1 1 2 2 2 1 3 3 2 1 0 2 -2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 2*a(n-2) + 2*a(n-3) - 3*a(n-5) - 3*a(n-6) - 2*a(n-7) + a(n-8) + 4*a(n-9) + 4*a(n-10) + a(n-11) - 2*a(n-12) - 3*a(n-13) - 3*a(n-14) + 2*a(n-16) + 2*a(n-17) - a(n-19).
Comments