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A010086 Weight distribution of d=3 Hamming code of length 31. 2
1, 0, 0, 155, 1085, 5208, 22568, 82615, 247845, 628680, 1383096, 2648919, 4414865, 6440560, 8280720, 9398115, 9398115, 8280720, 6440560, 4414865, 2648919, 1383096, 628680, 247845, 82615, 22568, 5208, 1085, 155, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
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
M. Terada, J. Asatani and T. Koumoto, Weight Distribution
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 = 31. - Georg Fischer, Apr 14 2020
EXAMPLE
Weight distribution:
i A_i
0 1
3 155
4 1085
5 5208
6 22568
7 82615
8 247845
9 628680
10 1383096
11 2648919
12 4414865
13 6440560
14 8280720
15 9398115
16 9398115
17 8280720
18 6440560
19 4414865
20 2648919
21 1383096
22 628680
23 247845
24 82615
25 22568
26 5208
27 1085
28 155
31 1
MATHEMATICA
m:=31; 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 *)
PROG
(PARI) Vecrev((1+x)^31 + 31*(1-x)*(1-x^2)^15)/32 \\ Andrew Howroyd, Jan 11 2021
CROSSREFS
Row 5 of A340030.
Sequence in context: A224336 A218328 A101535 * A110834 A110842 A289300
KEYWORD
nonn,fini,full
AUTHOR
STATUS
approved

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)