A208545 Number of 7-bead necklaces of n colors allowing reversal, with no adjacent beads having the same color.

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.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

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

Adjacent sequences: A208542 A208543 A208544 * A208546 A208547 A208548

Keyword

nonn,easy

Author

R. H. Hardin, Feb 27 2012

Status

approved