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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 Adjacent sequences:  A010083 A010084 A010085 * A010087 A010088 A010089 KEYWORD nonn,fini,full AUTHOR STATUS approved

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