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A325820
Multiplication table for carryless product i X j in base 3 for i >= 0 and j >= 0, read by antidiagonals.
11
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, 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, 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
OFFSET
0,8
EXAMPLE
The array begins as:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
0, 2, 1, 6, 8, 7, 3, 5, 4, 18, 20, 19, 24, ...
0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...
0, 4, 8, 12, 16, 11, 24, 19, 23, 36, 40, 44, 48, ...
0, 5, 7, 15, 11, 13, 21, 26, 19, 45, 50, 52, 33, ...
0, 6, 3, 18, 24, 21, 9, 15, 12, 54, 60, 57, 72, ...
0, 7, 5, 21, 19, 26, 15, 13, 11, 63, 70, 68, 57, ...
0, 8, 4, 24, 23, 19, 12, 11, 16, 72, 80, 76, 69, ...
0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, ...
0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 83, 120, ...
0, 11, 19, 33, 44, 52, 57, 68, 76, 99, 83, 91, 132, ...
0, 12, 24, 36, 48, 33, 72, 57, 69, 108, 120, 132, 144, ...
etc.
A(2,2) = 2*2 mod 3 = 1.
PROG
(PARI)
up_to = 105;
A325820sq(b, c) = fromdigits(Vec(Pol(digits(b, 3))*Pol(digits(c, 3)))%3, 3);
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); };
v325820 = A325820list(up_to);
A325820(n) = v325820[1+n];
CROSSREFS
Cf. A169999 (the main diagonal).
Row/Column 0: A000004, Row/Column 1: A001477, Row/Column 2: A004488, Row/Column 3: A008585, Row/Column 4: A242399, Row/Column 9: A008591.
Cf. A325821 (same table without the zero row and column).
Cf. A048720 (binary), A059692 (decimal), A004247 (full multiply).
Sequence in context: A352909 A323473 A341288 * A109042 A322403 A128540
KEYWORD
nonn,base,tabl
AUTHOR
Antti Karttunen, May 22 2019
STATUS
approved