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 A010088 Weight distribution of d=3 Hamming code of length 127. 3
 1, 0, 0, 2667, 82677, 1984248, 40346376, 698136399, 10472045985, 138455313640, 1633772700952, 17377481697723, 167982323077989, 1485996809606736, 12100259735369136, 91155294690805839 (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..127 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 = 127. - Georg Fischer, Apr 14 2020 EXAMPLE The weight distribution is: i A_i 0 1 3 2667 4 82677 5 1984248 6 40346376 7 698136399 8 10472045985 9 138455313640 10 1633772700952 11 17377481697723 12 167982323077989 13 1485996809606736 14 12100259735369136 15 91155294690805839 16 638087062835640873 17 4166333146052853552 18 25460924781434105040 19 146065305483269160835 20 788752649609653468509 21 4018882547238172355016 22 19363706818511194074168 23 88399531131386119148007 24 383064634902673182974697 25 1578226295785457917668888 26 6191503160389104138547176 27 23160808118541815153990579 28 82717171851935054121394925 29 282379310804718006044407200 30 922439081962078819745063520 31 2886341643559263104694304455 32 8659024930677789314082913365 33 24927496012555862201427876960 34 68917194858242677851006483360 35 183122832051905648227574489415 36 467980570799314434359357028505 37 1150979241695602290812068499320 38 2726003467173794899291741182600 39 6220879707140218581918768313275 40 13685935355708480880221290289205 41 29040887218210637159315728230120 42 59464673827764637992884586375960 43 117546448264185993885197347489815 44 224406855777082351962649481571465 45 413905978433285078143161128429360 46 737832396337595139298678533287120 47 1271583491560536557879927855087355 48 2119305819267560929799879758478925 49 3416839994329332521610566413573200 50 5330270391153758733712483605174192 51 8047663139585087324166406321172943 52 11761969204008973781473978469406609 53 16644296043408924306591066468540936 54 22808850133560377753476646642074616 55 30273564722725593421190356524797059 56 38923154643504334398673315531881933 57 48483227713838730919011449081237592 58 58514240344288123522944852339424680 59 68431908199252213890524837937373695 60 77556162625819175742594816329023521 61 85184637638194830580902393173363904 62 90680420711626755134508999184548672 63 93559164226281574604995522172224803 64 93559164226281574604995522172224803 65 90680420711626755134508999184548672 66 85184637638194830580902393173363904 67 77556162625819175742594816329023521 68 68431908199252213890524837937373695 69 58514240344288123522944852339424680 70 48483227713838730919011449081237592 71 38923154643504334398673315531881933 72 30273564722725593421190356524797059 73 22808850133560377753476646642074616 74 16644296043408924306591066468540936 75 11761969204008973781473978469406609 76 8047663139585087324166406321172943 77 5330270391153758733712483605174192 78 3416839994329332521610566413573200 79 2119305819267560929799879758478925 80 1271583491560536557879927855087355 81 737832396337595139298678533287120 82 413905978433285078143161128429360 83 224406855777082351962649481571465 84 117546448264185993885197347489815 85 59464673827764637992884586375960 86 29040887218210637159315728230120 87 13685935355708480880221290289205 88 6220879707140218581918768313275 89 2726003467173794899291741182600 90 1150979241695602290812068499320 91 467980570799314434359357028505 92 183122832051905648227574489415 93 68917194858242677851006483360 94 24927496012555862201427876960 95 8659024930677789314082913365 96 2886341643559263104694304455 97 922439081962078819745063520 98 282379310804718006044407200 99 82717171851935054121394925 100 23160808118541815153990579 101 6191503160389104138547176 102 1578226295785457917668888 103 383064634902673182974697 104 88399531131386119148007 105 19363706818511194074168 106 4018882547238172355016 107 788752649609653468509 108 146065305483269160835 109 25460924781434105040 110 4166333146052853552 111 638087062835640873 112 91155294690805839 113 12100259735369136 114 1485996809606736 115 167982323077989 116 17377481697723 117 1633772700952 118 138455313640 119 10472045985 120 698136399 121 40346376 122 1984248 123 82677 124 2667 127 1 MATHEMATICA m:=127; 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 *) CROSSREFS Row 7 of A340030. Sequence in context: A110838 A019424 A151813 * A252301 A250855 A235253 Adjacent sequences:  A010085 A010086 A010087 * A010089 A010090 A010091 KEYWORD nonn,fini,full AUTHOR N. J. A. Sloane. Entry revised Jul 18 2009 STATUS approved

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)