cp's OEIS Frontend

A193139 Number of symmetric satins of order n.

%I A193139 #18 Dec 25 2018 06:46:15
%S A193139 0,0,0,0,0,1,0,0,0,1,0,0,1,1,0,0,0,1,1,0,0,3,0,0,0,1,0,1,0,1,1,0,1,1,
%T A193139 0,0,1,3,0,1,0,1,1,0,0,3,0,0,1,1,0,0,1,3,1,0,0,3,0,0,1,1,1,1,0,1,1,1,
%U A193139 0,3,0,0,1,1,1,1,0,3,0,0,0,3,1,0,1,3,0,1,1,1,1,0,1,3,0,0,1,1,0,1,0,3,3,0,0,1,0,1,1,3,0,1,1,1,1,0,1,7
%N A193139 Number of symmetric satins of order n.
%H A193139 B. Grünbaum and G. C. Shephard, <a href="http://www.jstor.org/stable/2690105">Satins and twills: an introduction to the geometry of fabrics</a>, Math. Mag., 53 (1980), 139-161. See Theorem 5.
%F A193139 a(n) = A157230(n) - 1. - _Andrey Zabolotskiy_, Dec 25 2018
%p A193139 V:=proc(n) local j,i,t1,t2,al,even;
%p A193139 t1:=ifactors(n)[2];
%p A193139 t2:=nops(t1);
%p A193139 if (n mod 2) = 0 then even:=1; al:=t1[1][2]; else even:=0; al:=0; fi;
%p A193139 j:=t2-even;
%p A193139 if (al <= 1) then RETURN(2^(j-1)-1); fi;
%p A193139 if (al = 2) then RETURN(2^j-1); fi;
%p A193139 if (al >= 3) then RETURN(2^(j+1)-1); fi;
%p A193139 end;
%p A193139 [seq(V(n),n=3..120)];
%Y A193139 Cf. A193138, A193140, A157230.
%K A193139 nonn
%O A193139 3,22
%A A193139 _N. J. A. Sloane_, Jul 16 2011