A213331 Number of isomorphism classes of reduced Witt rings of fields with 2n orderings.

1, 2, 3, 6, 9, 16, 24, 42, 64, 105, 159, 258, 390, 614, 925, 1441, 2162, 3317, 4951, 7526, 11191, 16841, 24923, 37253, 54912, 81493, 119629, 176549, 258205, 379025, 552280, 807014, 1171959, 1705148, 2468113, 3577332, 5162240, 7455485, 10727083, 15442040, 22157247, 31798821, 45507039, 65124514, 92967787, 132690935

Offset

1,2

Comments

The number with 2n+1 orderings is the same as the number with 2n orderings (cf. A213332).

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..400

Thomas C. Craven, An application of Pólya's theory of counting to an enumeration problem arising in quadratic form theory, J. Combin. Theory Ser. A 29 (1980), no. 2, 174--181. MR0583956 (81j:10027).

Maple

read transforms;
w:=proc(n) option remember; global did; local v; # did(n, d)=1 if d|n otherwise 0
if n=1 then 1 elif (n mod 2) = 1 then w(n-1);
else v:=n/2;
(1/n)* ( add(2*i*w(i)*did(v, i), i=1..v) +
add( add(2*i*w(i)*w(n-2*k)*did(k, i), i=1..k), k=1..v-1));
fi; end;
[seq(w(2*n), n=1..50)];

Crossrefs

Cf. A213332.

Sequence in context: A357640 A007865 A052812 * A218153 A319642 A062114

Adjacent sequences: A213328 A213329 A213330 * A213332 A213333 A213334

Keyword

nonn

Author

N. J. A. Sloane, Jun 08 2012

Status

approved