A193139 Number of symmetric satins of order n.

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, 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, 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

Offset: 3

Author

N. J. A. Sloane, Jul 16 2011

Keywords

• nonn

Links

• B. Grünbaum and G. C. Shephard, Satins and twills: an introduction to the geometry of fabrics, Math. Mag., 53 (1980), 139-161. See Theorem 5.

Crossrefs

Cf. A193138, A193140, A157230.

Programs

Maple

V:=proc(n) local j,i,t1,t2,al,even;
t1:=ifactors(n)[2];
t2:=nops(t1);
if (n mod 2) = 0 then even:=1; al:=t1[1][2]; else even:=0; al:=0; fi;
j:=t2-even;
if (al <= 1) then RETURN(2^(j-1)-1); fi;
if (al = 2) then RETURN(2^j-1); fi;
if (al >= 3) then RETURN(2^(j+1)-1); fi;
end;
[seq(V(n),n=3..120)];

Formula

a(n) = A157230(n) - 1. - Andrey Zabolotskiy, Dec 25 2018