A028363 Total number of doubly-even self-dual binary codes of length 8n.

1, 30, 9845550, 171634285407048750, 193419995622362136809061156168750, 14272693289804307141953423466197932293533748208968750

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

References

• F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 631.

Crossrefs

Cf. A003178, A003179, A028362.

Programs

Mathematica

Join[{1},Table[2*Product[2^i+1,{i,4n-2}],{n,6}]] (* Harvey P. Dale, May 08 2013 *)
Table[Product[2^i + 1, {i, 0, n/2 - 2}], {n, 8, 40, 8}] (* Nathan J. Russell, Mar 04 2016 *)

Python

for n in range(8, 50, 8):
    product = 1
    for i in range(n//2 - 1):
        product *= 2**i + 1
    print(product, end=", ")
# Nathan J. Russell, Mar 01 2016

Formula

a(n) = 2*Product_{i=1..4n-2} (2^i + 1).

Extensions

There is an error in Eq. (75) of F. J. MacWilliams and N. J. A. Sloane, the lower subscript should be 1 not 0.

Formula corrected by N. J. A. Sloane, May 07 2013 following a suggestion from Harvey P. Dale