A056456 Number of palindromes of length n using exactly five different symbols.

0, 0, 0, 0, 0, 0, 0, 0, 120, 120, 1800, 1800, 16800, 16800, 126000, 126000, 834120, 834120, 5103000, 5103000, 29607600, 29607600, 165528000, 165528000, 901020120, 901020120, 4809004200, 4809004200, 25292030400

Offset

1,9

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 (1,14,-14,-71,71,154,-154,-120,120).

Formula

a(n) = 5! * Stirling2( [(n+1)/2], 5).

G.f.: -120*x^9/((x-1)*(2*x-1)*(2*x+1)*(2*x^2-1)*(3*x^2-1)*(5*x^2-1)). - Colin Barker, Sep 03 2012

G.f.: k!(x^(2k-1)+x^(2k))/Product_{i=1..k}(1-ix^2), where k=5 is the number of symbols. - Robert A. Russell, Sep 25 2018

Mathematica

k=5; Table[k! StirlingS2[Ceiling[n/2], k], {n, 1, 30}] (* Robert A. Russell, Sep 25 2018 *)
LinearRecurrence[{1, 14, -14, -71, 71, 154, -154, -120, 120}, {0, 0, 0, 0, 0, 0, 0, 0, 120}, 30] (* Vincenzo Librandi, Sep 29 2018 *)

Prog

(PARI) a(n) = 5!*stirling((n+1)\2, 5, 2); \\ Altug Alkan, Sep 25 2018

Crossrefs

Cf. A056451, A001118.

Sequence in context: A332560 A334571 A056466 * A239535 A085218 A296884

Adjacent sequences: A056453 A056454 A056455 * A056457 A056458 A056459

Keyword

nonn,easy

Author

Marks R. Nester

Status

approved