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A209033
Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.
1
2, 11, 34, 88, 187, 358, 625, 1023, 1584, 2355, 3374, 4700, 6377, 8476, 11049, 14175, 17916, 22361, 27580, 33672, 40713, 48816, 58063, 68577, 80448, 93809, 108760, 125442, 143963, 164476, 187095, 211985, 239266, 269115, 301660, 337086, 375531
OFFSET
1,1
COMMENTS
Row 5 of A209032.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) - 2*a(n-6) + 2*a(n-7) + a(n-8) - 2*a(n-9) + 2*a(n-10) - 2*a(n-12) + a(n-13).
Empirical g.f.: x*(2 + 7*x + 12*x^2 + 24*x^3 + 29*x^4 + 32*x^5 + 32*x^6 + 23*x^7 + 12*x^8 + 9*x^9 - x^11 + x^12) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Jul 07 2018
EXAMPLE
Some solutions for n=6;
-2 -5 -2 -5 -3 -4 -6 -4 -3 -1 -6 -3 -2 -4 -1 -2
0 -1 0 -1 0 0 -1 -1 0 -1 -1 -1 -2 0 0 -2
-1 0 -2 2 0 3 5 3 -3 -1 4 0 3 -1 0 -1
-1 5 0 4 0 0 2 1 3 -1 4 4 -2 3 0 3
4 1 4 0 3 1 0 1 3 4 -1 0 3 2 1 2
CROSSREFS
Cf. A209032.
Sequence in context: A088306 A100109 A328152 * A222650 A026961 A026971
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 04 2012
STATUS
approved