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

%I

%S 1,0,0,651,9765,109368,1057224,8649279,60544953,369776680,1996794072,

%T 9621890019,41694856749,163568562192,584173436400,1908310936455,

%U 5724932809365,15827726179440,40448633569680

%N Weight distribution of d=3 Hamming code of length 63.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 129.

%H Georg Fischer, <a href="/A010087/b010087.txt">Table of n, a(n) for n = 0..63</a>

%H 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 <a href="/wiki/List_of_weight_distributions">List of weight distributions</a>

%F 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 The weight distribution is:

%e i A_i

%e 0 1

%e 3 651

%e 4 9765

%e 5 109368

%e 6 1057224

%e 7 8649279

%e 8 60544953

%e 9 369776680

%e 10 1996794072

%e 11 9621890019

%e 12 41694856749

%e 13 163568562192

%e 14 584173436400

%e 15 1908310936455

%e 16 5724932809365

%e 17 15827726179440

%e 18 40448633569680

%e 19 95799462143175

%e 20 210758816714985

%e 21 431553634502760

%e 22 823875120414360

%e 23 1468647185710635

%e 24 2447745309517725

%e 25 3818482327223928

%e 26 5580858785942664

%e 27 7647844002734159

%e 28 9832942289229633

%e 29 11867343566087520

%e 30 13449656041565856

%e 31 14317376396958243

%e 32 14317376396958243

%e 33 13449656041565856

%e 34 11867343566087520

%e 35 9832942289229633

%e 36 7647844002734159

%e 37 5580858785942664

%e 38 3818482327223928

%e 39 2447745309517725

%e 40 1468647185710635

%e 41 823875120414360

%e 42 431553634502760

%e 43 210758816714985

%e 44 95799462143175

%e 45 40448633569680

%e 46 15827726179440

%e 47 5724932809365

%e 48 1908310936455

%e 49 584173436400

%e 50 163568562192

%e 51 41694856749

%e 52 9621890019

%e 53 1996794072

%e 54 369776680

%e 55 60544953

%e 56 8649279

%e 57 1057224

%e 58 109368

%e 59 9765

%e 60 651

%e 63 1

%t m:=63; RecurrenceTable[{a[n]==(Binomial[m,n-1]-a[n-1]-(m-n+2)*a[n-2])/n,

%t a[0]==1,a[1]==0}, a,{n,0,m}] (* _Georg Fischer, Apr 14 2020 *)

%o (PARI) Vecrev((1+x)^63 + 63*(1-x)*(1-x^2)^31)/64 \\ _Andrew Howroyd_, Jan 11 2021

%Y Row 6 of A340030.

%K nonn,fini,full

%O 0,4

%A _N. J. A. Sloane_

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)