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

1,7

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..34.

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A056450, A000919.

Sequence in context: A004011 A334570 A056465 * A128378 A165845 A189049

Adjacent sequences: A056452 A056453 A056454 * A056456 A056457 A056458

Keyword

nonn,easy

Author

Marks R. Nester

Status

approved