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%I #25 Sep 27 2022 19:17:51
%S 0,0,0,0,1,0,0,2,2,0,0,3,1,3,0,0,4,6,6,4,0,0,5,8,9,8,5,0,0,6,7,12,12,
%T 7,6,0,0,7,3,15,16,15,3,7,0,0,8,5,18,11,11,18,5,8,0,0,9,4,21,24,13,24,
%U 21,4,9,0,0,10,18,24,19,21,21,19,24,18,10,0,0,11,20,27,23,26,9,26,23,27,20,11,0,0,12,19,30,36,19,15,15,19,36,30,19,12,0
%N Multiplication table for carryless product i X j in base 3 for i >= 0 and j >= 0, read by antidiagonals.
%H Antti Karttunen, <a href="/A325820/b325820.txt">Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array</a>
%H <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>
%e The array begins as:
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
%e 0, 2, 1, 6, 8, 7, 3, 5, 4, 18, 20, 19, 24, ...
%e 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...
%e 0, 4, 8, 12, 16, 11, 24, 19, 23, 36, 40, 44, 48, ...
%e 0, 5, 7, 15, 11, 13, 21, 26, 19, 45, 50, 52, 33, ...
%e 0, 6, 3, 18, 24, 21, 9, 15, 12, 54, 60, 57, 72, ...
%e 0, 7, 5, 21, 19, 26, 15, 13, 11, 63, 70, 68, 57, ...
%e 0, 8, 4, 24, 23, 19, 12, 11, 16, 72, 80, 76, 69, ...
%e 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, ...
%e 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 83, 120, ...
%e 0, 11, 19, 33, 44, 52, 57, 68, 76, 99, 83, 91, 132, ...
%e 0, 12, 24, 36, 48, 33, 72, 57, 69, 108, 120, 132, 144, ...
%e etc.
%e A(2,2) = 2*2 mod 3 = 1.
%o (PARI)
%o up_to = 105;
%o A325820sq(b, c) = fromdigits(Vec(Pol(digits(b,3))*Pol(digits(c,3)))%3, 3);
%o A325820list(up_to) = { my(v = vector(up_to), i=0); for(a=0,oo, for(col=0,a, if(i++ > up_to, return(v)); v[i] = A325820sq(a-col,col))); (v); };
%o v325820 = A325820list(up_to);
%o A325820(n) = v325820[1+n];
%Y Cf. A169999 (the main diagonal).
%Y Row/Column 0: A000004, Row/Column 1: A001477, Row/Column 2: A004488, Row/Column 3: A008585, Row/Column 4: A242399, Row/Column 9: A008591.
%Y Cf. A007089, A207669, A207670, A263273, A325825.
%Y Cf. A325821 (same table without the zero row and column).
%Y Cf. A048720 (binary), A059692 (decimal), A004247 (full multiply).
%K nonn,base,tabl
%O 0,8
%A _Antti Karttunen_, May 22 2019
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