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A010086 Weight distribution of d=3 Hamming code of length 31.

%I A010086 #14 Jan 11 2021 13:21:17
%S A010086 1,0,0,155,1085,5208,22568,82615,247845,628680,1383096,2648919,
%T A010086 4414865,6440560,8280720,9398115,9398115,8280720,6440560,4414865,
%U A010086 2648919,1383096,628680,247845,82615,22568,5208,1085,155,0,0,1
%N A010086 Weight distribution of d=3 Hamming code of length 31.
%D A010086 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 129.
%H A010086 M. Terada, J. Asatani and T. Koumoto, <a href="http://isec.ec.okayama-u.ac.jp/home/kusaka/wd/index.html">Weight Distribution</a>
%H A010086 <a href="/wiki/List_of_weight_distributions">List of weight distributions</a>
%F A010086 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
%e A010086 Weight distribution:
%e A010086 i A_i
%e A010086 0 1
%e A010086 3 155
%e A010086 4 1085
%e A010086 5 5208
%e A010086 6 22568
%e A010086 7 82615
%e A010086 8 247845
%e A010086 9 628680
%e A010086 10 1383096
%e A010086 11 2648919
%e A010086 12 4414865
%e A010086 13 6440560
%e A010086 14 8280720
%e A010086 15 9398115
%e A010086 16 9398115
%e A010086 17 8280720
%e A010086 18 6440560
%e A010086 19 4414865
%e A010086 20 2648919
%e A010086 21 1383096
%e A010086 22 628680
%e A010086 23 247845
%e A010086 24 82615
%e A010086 25 22568
%e A010086 26 5208
%e A010086 27 1085
%e A010086 28 155
%e A010086 31 1
%t A010086 m:=31; RecurrenceTable[{a[n]==(Binomial[m,n-1]-a[n-1]-(m-n+2)*a[n-2])/n,
%t A010086 a[0]==1,a[1]==0}, a, {n,0,127}] (* _Georg Fischer_, Apr 14 2020 *)
%o A010086 (PARI) Vecrev((1+x)^31 + 31*(1-x)*(1-x^2)^15)/32 \\ _Andrew Howroyd_, Jan 11 2021
%Y A010086 Row 5 of A340030.
%K A010086 nonn,fini,full
%O A010086 0,4
%A A010086 _N. J. A. Sloane_