A056455 Palindromes using exactly four different symbols.

0, 0, 0, 0, 0, 0, 24, 24, 240, 240, 1560, 1560, 8400, 8400, 40824, 40824, 186480, 186480, 818520, 818520, 3498000, 3498000, 14676024, 14676024, 60780720, 60780720, 249401880, 249401880, 1016542800, 1016542800, 4123173624, 4123173624, 16664094960, 16664094960

Offset: 1

Author

Marks R. Nester

Keywords

• nonn
• easy

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

• Index entries for linear recurrences with constant coefficients, signature (1,9,-9,-26,26,24,-24).

Crossrefs

Cf. A056450, A000919.

Programs

Mathematica

k=4; Table[k! StirlingS2[Ceiling[n/2],k],{n,1,30}] (* Robert A. Russell, Sep 25 2018 *)

PARI

a(n) = 4!*stirling((n+1)\2, 4, 2); \\ Altug Alkan, Sep 25 2018

Formula

a(n) = 4! * Stirling2( [(n+1)/2], 4).

G.f.: 24*x^7/((1-x)*(1-2*x)*(1+2*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-ix^2), where k=4 is the number of symbols. - Robert A. Russell, Sep 25 2018