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A056473 Number of palindromic structures using exactly four different symbols. 1


%S 0,0,0,0,0,0,1,1,10,10,65,65,350,350,1701,1701,7770,7770,34105,34105,

%T 145750,145750,611501,611501,2532530,2532530,10391745,10391745,

%U 42355950,42355950,171798901

%N Number of palindromic structures using exactly four different symbols.

%C Permuting the symbols will not change the structure.

%D 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]

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,9,-9,-26,26,24,-24).

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

%F 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]

%F 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

%t 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 *)

%Y Cf. A000453, A007581.

%K nonn,easy

%O 1,9

%A _Marks R. Nester_

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