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

1,9

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

Table of n, a(n) for n=1..31.

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

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

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 *)

Crossrefs

Cf. A000453, A007581.

Sequence in context: A270012 A219911 A056483 * A241869 A243126 A377189

Adjacent sequences: A056470 A056471 A056472 * A056474 A056475 A056476

Keyword

nonn,easy

Author

Marks R. Nester

Status

approved