A056454 Number of palindromes of length n using exactly three different symbols.

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.]

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

Marks R. Nester

Status

approved