A056455 - OEIS

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

(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