A010088 Weight distribution of d=3 Hamming code of length 127.

1, 0, 0, 2667, 82677, 1984248, 40346376, 698136399, 10472045985, 138455313640, 1633772700952, 17377481697723, 167982323077989, 1485996809606736, 12100259735369136, 91155294690805839

Offset

0,4

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 129.

Links

Georg Fischer, Table of n, a(n) for n = 0..127

M. Terada, J. Asatani and T. Koumoto, Weight Distribution

List of weight distributions

Formula

Recurrence: a(n) = (binomial(m,n-1) - a(n-1) - (m-n+2)*a(n-2))/n for n > 1, a(0)=1, a(1)=0 with m = 127. - Georg Fischer, Apr 14 2020

Mathematica

m:=127; RecurrenceTable[{a[n]==(Binomial[m, n-1]-a[n-1]-(m-n+2)*a[n-2])/n,
a[0]==1, a[1]==0}, a, {n, 0, 127}] (* Georg Fischer, Apr 14 2020 *)

Crossrefs

Row 7 of A340030.

Sequence in context: A110838 A019424 A151813 * A252301 A250855 A235253

Adjacent sequences: A010085 A010086 A010087 * A010089 A010090 A010091

Keyword

nonn,fini,full

Author

N. J. A. Sloane

Extensions

Entry revised by N. J. A. Sloane, Jul 18 2009

Status

approved