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A208545
Number of 7-bead necklaces of n colors allowing reversal, with no adjacent beads having the same color.
1
0, 0, 9, 156, 1170, 5580, 19995, 58824, 149796, 341640, 714285, 1391940, 2559414, 4482036, 7529535, 12204240, 19173960, 29309904, 43730001, 63847980, 91428570, 128649180, 178168419, 243201816, 327605100, 435965400, 573700725, 747168084
OFFSET
1,3
COMMENTS
Row 7 of A208544.
FORMULA
Empirical: a(n) = (1/14)*n^7 - (1/2)*n^6 + (3/2)*n^5 - (5/2)*n^4 + (5/2)*n^3 - (3/2)*n^2 + (3/7)*n.
From Colin Barker, Nov 11 2017: (Start)
G.f.: 3*x^3*(3 + 28*x + 58*x^2 + 28*x^3 + 3*x^4) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
EXAMPLE
All solutions for n=3
..1....1....1....1....1....1....1....1....1
..2....2....2....2....2....2....2....2....2
..3....3....1....1....3....1....3....1....3
..1....1....2....2....1....2....2....3....2
..2....3....3....3....3....1....3....1....3
..3....1....1....2....2....2....2....2....1
..2....3....3....3....3....3....3....3....3
PROG
(PARI) Vec(3*x^3*(3 + 28*x + 58*x^2 + 28*x^3 + 3*x^4) / (1 - x)^8 + O(x^40)) \\ Colin Barker, Nov 11 2017
CROSSREFS
Cf. A208537.
Sequence in context: A208998 A236578 A305139 * A183471 A109677 A320290
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Feb 27 2012
STATUS
approved