cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A010087 Weight distribution of d=3 Hamming code of length 63.

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%I A010087 #14 Jan 11 2021 13:21:07
%S A010087 1,0,0,651,9765,109368,1057224,8649279,60544953,369776680,1996794072,
%T A010087 9621890019,41694856749,163568562192,584173436400,1908310936455,
%U A010087 5724932809365,15827726179440,40448633569680
%N A010087 Weight distribution of d=3 Hamming code of length 63.
%D A010087 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 129.
%H A010087 Georg Fischer, <a href="/A010087/b010087.txt">Table of n, a(n) for n = 0..63</a>
%H A010087 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 A010087 <a href="/wiki/List_of_weight_distributions">List of weight distributions</a>
%F A010087 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 = 63. - _Georg Fischer_, Apr 14 2020
%e A010087 The weight distribution is:
%e A010087 i A_i
%e A010087 0 1
%e A010087 3 651
%e A010087 4 9765
%e A010087 5 109368
%e A010087 6 1057224
%e A010087 7 8649279
%e A010087 8 60544953
%e A010087 9 369776680
%e A010087 10 1996794072
%e A010087 11 9621890019
%e A010087 12 41694856749
%e A010087 13 163568562192
%e A010087 14 584173436400
%e A010087 15 1908310936455
%e A010087 16 5724932809365
%e A010087 17 15827726179440
%e A010087 18 40448633569680
%e A010087 19 95799462143175
%e A010087 20 210758816714985
%e A010087 21 431553634502760
%e A010087 22 823875120414360
%e A010087 23 1468647185710635
%e A010087 24 2447745309517725
%e A010087 25 3818482327223928
%e A010087 26 5580858785942664
%e A010087 27 7647844002734159
%e A010087 28 9832942289229633
%e A010087 29 11867343566087520
%e A010087 30 13449656041565856
%e A010087 31 14317376396958243
%e A010087 32 14317376396958243
%e A010087 33 13449656041565856
%e A010087 34 11867343566087520
%e A010087 35 9832942289229633
%e A010087 36 7647844002734159
%e A010087 37 5580858785942664
%e A010087 38 3818482327223928
%e A010087 39 2447745309517725
%e A010087 40 1468647185710635
%e A010087 41 823875120414360
%e A010087 42 431553634502760
%e A010087 43 210758816714985
%e A010087 44 95799462143175
%e A010087 45 40448633569680
%e A010087 46 15827726179440
%e A010087 47 5724932809365
%e A010087 48 1908310936455
%e A010087 49 584173436400
%e A010087 50 163568562192
%e A010087 51 41694856749
%e A010087 52 9621890019
%e A010087 53 1996794072
%e A010087 54 369776680
%e A010087 55 60544953
%e A010087 56 8649279
%e A010087 57 1057224
%e A010087 58 109368
%e A010087 59 9765
%e A010087 60 651
%e A010087 63 1
%t A010087 m:=63; RecurrenceTable[{a[n]==(Binomial[m,n-1]-a[n-1]-(m-n+2)*a[n-2])/n,
%t A010087 a[0]==1,a[1]==0}, a,{n,0,m}] (* _Georg Fischer, Apr 14 2020 *)
%o A010087 (PARI) Vecrev((1+x)^63 + 63*(1-x)*(1-x^2)^31)/64 \\ _Andrew Howroyd_, Jan 11 2021
%Y A010087 Row 6 of A340030.
%K A010087 nonn,fini,full
%O A010087 0,4
%A A010087 _N. J. A. Sloane_