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A047774 Number of dissectable polyhedra with symmetry of type C. 2

%I

%S 0,0,0,0,0,0,1,1,0,5,6,0,26,32,0,133,176,0,708,952,0,3861,5302,0,

%T 21604,29960,0,123266,172535,0,715221,1007575,0,4206956,5959656,0,

%U 25032840,35622384,0,150413348,214875099,0,911379384,1306303424,0,5562367173

%N Number of dissectable polyhedra with symmetry of type C.

%H L. W. Beineke and R. E. Pippert, <a href="http://dx.doi.org/10.4153/CJM-1974-006-x">Enumerating dissectable polyhedra by their automorphism groups</a>, Canad. J. Math., 26 (1974), 50-67.

%F Reference gives complicated recurrence.

%p # T=A001764

%p T := proc(n)

%p if n < 0 then

%p 0;

%p else

%p (3*n)!/n!/(2*n+1)! ;

%p end if;

%p end proc:

%p # U=A047749

%p U := proc(n)

%p if type(n,'integer') then

%p if type(n,'even') then

%p T(n/2) ;

%p else

%p (3*n-1)/(n+1)*T((n-1)/2) ;

%p end if;

%p else

%p 0 ;

%p end if;

%p end proc:

%p # V=A047750

%p V := proc(n)

%p if type(n,'integer') then

%p if type(n,'even') then

%p 2*U(n+1)-U(n) ;

%p else

%p 2*U(n+1) ;

%p end if;

%p else

%p 0;

%p end if;

%p end proc:

%p K := proc(n)

%p if n < 1 then

%p 0 ;

%p elif n = 1 then

%p 1;

%p else

%p U((n-5)/12) ;

%p end if;

%p end proc:

%p J := proc(n)

%p if type((n-5)/12,'integer') then

%p T((n-5)/12)-K(n) ;

%p %/2 ;

%p else

%p 0;

%p end if ;

%p end proc:

%p Q := proc(n)

%p if type((n-2)/6,'integer') then

%p U((n-2)/6) ;

%p else

%p 0 ;

%p end if;

%p end proc:

%p N := proc(n)

%p if type((n-2)/6,'integer') then

%p T((n-2)/6)-Q(n) ;

%p %/2 ;

%p else

%p 0;

%p end if ;

%p end proc:

%p DD := proc(n)

%p 2*U((n-1)/3)+V((n-2)/3)-2*K(n)-Q(n) ;

%p %/2 ;

%p end proc:

%p OO := proc(n)

%p if type((n-2)/6,'integer') then

%p T((n-2)/6)-Q(n) ;

%p %/2 ;

%p else

%p 0;

%p end if ;

%p end proc:

%p C := proc(n)

%p if n = 1 then

%p 0;

%p elif modp(n,3) = 1 then

%p T((n-1)/3)-DD(n) ;

%p %/2 ;

%p else

%p U((2*n-1)/3)-2*DD(n)-4*J(n) -2*K(n)-2*N(n)-2*OO(n)-Q(n) ;

%p %/4 ;

%p end if;

%p end proc:

%p seq(C(n),n=1..50) ; # _R. J. Mathar_, Jul 10 2013

%Y Cf. A027610.

%K nonn,easy

%O 1,10

%A _N. J. A. Sloane_.

%E More terms from _R. J. Mathar_, Jul 10 2013

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Last modified February 17 12:32 EST 2020. Contains 331996 sequences. (Running on oeis4.)