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

3,22

Links

Table of n, a(n) for n=3..120.

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.

Formula

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

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)];

Crossrefs

Cf. A193138, A193140, A157230.

Sequence in context: A128980 A143276 A096693 * A378440 A378439 A083206

Adjacent sequences: A193136 A193137 A193138 * A193140 A193141 A193142

Keyword

nonn

Author

N. J. A. Sloane, Jul 16 2011

Status

approved