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 A010087 Weight distribution of d=3 Hamming code of length 63. 3
 1, 0, 0, 651, 9765, 109368, 1057224, 8649279, 60544953, 369776680, 1996794072, 9621890019, 41694856749, 163568562192, 584173436400, 1908310936455, 5724932809365, 15827726179440, 40448633569680 (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 Georg Fischer, Table of n, a(n) for n = 0..63 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 = 63. - Georg Fischer, Apr 14 2020 EXAMPLE The weight distribution is: i A_i 0 1 3 651 4 9765 5 109368 6 1057224 7 8649279 8 60544953 9 369776680 10 1996794072 11 9621890019 12 41694856749 13 163568562192 14 584173436400 15 1908310936455 16 5724932809365 17 15827726179440 18 40448633569680 19 95799462143175 20 210758816714985 21 431553634502760 22 823875120414360 23 1468647185710635 24 2447745309517725 25 3818482327223928 26 5580858785942664 27 7647844002734159 28 9832942289229633 29 11867343566087520 30 13449656041565856 31 14317376396958243 32 14317376396958243 33 13449656041565856 34 11867343566087520 35 9832942289229633 36 7647844002734159 37 5580858785942664 38 3818482327223928 39 2447745309517725 40 1468647185710635 41 823875120414360 42 431553634502760 43 210758816714985 44 95799462143175 45 40448633569680 46 15827726179440 47 5724932809365 48 1908310936455 49 584173436400 50 163568562192 51 41694856749 52 9621890019 53 1996794072 54 369776680 55 60544953 56 8649279 57 1057224 58 109368 59 9765 60 651 63 1 MATHEMATICA m:=63; 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, m}] (* _Georg Fischer, Apr 14 2020 *) PROG (PARI) Vecrev((1+x)^63 + 63*(1-x)*(1-x^2)^31)/64 \\ Andrew Howroyd, Jan 11 2021 CROSSREFS Row 6 of A340030. Sequence in context: A255619 A151736 A346138 * A110850 A257715 A048915 Adjacent sequences:  A010084 A010085 A010086 * A010088 A010089 A010090 KEYWORD nonn,fini,full AUTHOR STATUS approved

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Last modified November 28 13:41 EST 2021. Contains 349412 sequences. (Running on oeis4.)