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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 (list; graph; refs; listen; history; text; internal format)
 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: A215557 A208998 A236578 * A183471 A109677 A024122 Adjacent sequences:  A208542 A208543 A208544 * A208546 A208547 A208548 KEYWORD nonn,easy AUTHOR R. H. Hardin, Feb 27 2012 STATUS approved

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Last modified March 18 11:11 EDT 2018. Contains 300749 sequences. (Running on oeis4.)