A056473 Number of palindromic structures using exactly four different symbols.

0, 0, 0, 0, 0, 0, 1, 1, 10, 10, 65, 65, 350, 350, 1701, 1701, 7770, 7770, 34105, 34105, 145750, 145750, 611501, 611501, 2532530, 2532530, 10391745, 10391745, 42355950, 42355950, 171798901

Offset: 1

Author

Marks R. Nester

Keywords

• nonn
• easy

Comments

Permuting the symbols will not change the structure.

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. A000453, A007581.

Programs

Mathematica

StirlingS2[Floor[(Range[40]+1)/2],4] (* or *) LinearRecurrence[ {1,9,-9,-26,26,24,-24},{0,0,0,0,0,0,1},40] (* Harvey P. Dale, Mar 08 2013 *)

Formula

stirling2( [(n+1)/2], 4).

G.f.: x^7/((x-1)*(2*x-1)*(2*x+1)*(2*x^2-1)*(3*x^2-1)). [Colin Barker, Jul 24 2012]

a(1)=a(2)=a(3)=a(4)=a(5)=a(6)=0, a(7)=1, a(n)=a(n-1)+9*a(n-2)-9*a(n-3)- 26*a(n-4)+ 26*a(n-5)+24*a(n-6)-24*a (n-7). - Harvey P. Dale, Mar 08 2013