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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

Table of n, a(n) for n=0..31.

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 = 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

Adjacent sequences:  A010083 A010084 A010085 * A010087 A010088 A010089

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 2 17:56 EST 2021. Contains 349445 sequences. (Running on oeis4.)