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A056455 Palindromes using exactly four different symbols. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A103640 A004011 A056465 * A128378 A165845 A189049

Adjacent sequences:  A056452 A056453 A056454 * A056456 A056457 A056458

KEYWORD

nonn,easy

AUTHOR

Marks R. Nester

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)