A056457 Palindromes using exactly six different symbols.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 720, 720, 15120, 15120, 191520, 191520, 1905120, 1905120, 16435440, 16435440, 129230640, 129230640, 953029440, 953029440, 6711344640, 6711344640, 45674188560

Offset

1,11

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

Table of n, a(n) for n=1..27.

Index entries for linear recurrences with constant coefficients, signature (1,20,-20,-155,155,580,-580,-1044,1044,720,-720).

Formula

a(n) = 6! * Stirling2( [(n+1)/2], 6).

G.f.: 720*x^11/((x-1)*(2*x-1)*(2*x+1)*(2*x^2-1)*(3*x^2-1)*(5*x^2-1)*(6*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=6 is the number of symbols. - Robert A. Russell, Sep 25 2018

Mathematica

k=6; Table[k! StirlingS2[Ceiling[n/2], k], {n, 1, 30}]

Prog

(PARI) a(n) = 6!*stirling((n+1)\2, 6, 2); \\ Altug Alkan, Sep 25 2018

Crossrefs

Cf. A056452, A000920.

Sequence in context: A267026 A145226 A056467 * A068351 A067892 A337036

Adjacent sequences: A056454 A056455 A056456 * A056458 A056459 A056460

Keyword

nonn,easy

Author

Marks R. Nester

Status

approved