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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
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.]
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
Sequence in context: A256136 A111437 A056464 * A056452 A183622 A176861
KEYWORD
nonn,easy
STATUS
approved