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 A056454 Number of palindromes of length n using exactly three different symbols. 10
 0, 0, 0, 0, 6, 6, 36, 36, 150, 150, 540, 540, 1806, 1806, 5796, 5796, 18150, 18150, 55980, 55980, 171006, 171006, 519156, 519156, 1569750, 1569750, 4733820, 4733820, 14250606, 14250606, 42850116, 42850116, 128746950, 128746950, 386634060, 386634060, 1160688606 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 REFERENCES M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2.] LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-6,6). FORMULA a(n) = 3! * Stirling2( [(n+1)/2], 3). G.f.: 6*x^5/((1-x)*(1-2*x^2)*(1-3*x^2)). - Colin Barker, May 05 2012 G.f.: k!(x^(2k-1)+x^(2k))/Product_{i=1..k}(1-i*x^2), where k=3 is the number of symbols. - Robert A. Russell, Sep 25 2018 MAPLE with(combinat, stirling2): A056454:=n->3!*stirling2(floor((n+1)/2), 3); # (C. Ronaldo) MATHEMATICA LinearRecurrence[{1, 5, -5, -6, 6}, {0, 0, 0, 0, 6}, 40] (* Harvey P. Dale, Sep 02 2016 *) k=3; Table[k! StirlingS2[Ceiling[n/2], k], {n, 1, 30}] (* Robert A. Russell, Sep 25 2018 *) PROG (PARI) a(n) = 3!*stirling((n+1)\2, 3, 2); \\ Altug Alkan, Sep 25 2018 (MAGMA) [StirlingSecond((n+1) div 2, 3)*Factorial(3): n in [1..40]]; // Vincenzo Librandi, Sep 26 2018 CROSSREFS Cf. A056449, A001117. Sequence in context: A256136 A111437 A056464 * A056452 A183622 A176861 Adjacent sequences:  A056451 A056452 A056453 * A056455 A056456 A056457 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 24 14:49 EDT 2019. Contains 323532 sequences. (Running on oeis4.)