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A061858 Differences between the ordinary multiplication table A004247 and the carryless multiplication table for GF(2)[X] polynomials A048720, i.e., the effect of the carry bits in binary multiplication.

%I A061858 #13 Feb 14 2021 13:16:33
%S A061858 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,
%T A061858 0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,8,0,0,0,0,0,0,12,0,8,0,12,0,0,0,0,
%U A061858 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,16,8,0,0,0,0,0,0,0,0,0,0,0,24,24,0,0,0
%N A061858 Differences between the ordinary multiplication table A004247 and the carryless multiplication table for GF(2)[X] polynomials A048720, i.e., the effect of the carry bits in binary multiplication.
%F A061858 a(n) = A004247(n) - A048720(n).
%e A061858 From _Peter Munn_, Jan 28 2021: (Start)
%e A061858 The top left 12 X 12 corner of the table:
%e A061858       |  0   1   2   3   4   5   6   7   8   9  10  11
%e A061858 ------+------------------------------------------------
%e A061858    0  |  0   0   0   0   0   0   0   0   0   0   0   0
%e A061858    1  |  0   0   0   0   0   0   0   0   0   0   0   0
%e A061858    2  |  0   0   0   0   0   0   0   0   0   0   0   0
%e A061858    3  |  0   0   0   4   0   0   8  12   0   0   0   4
%e A061858    4  |  0   0   0   0   0   0   0   0   0   0   0   0
%e A061858    5  |  0   0   0   0   0   8   0   8   0   0  16  16
%e A061858    6  |  0   0   0   8   0   0  16  24   0   0   0   8
%e A061858    7  |  0   0   0  12   0   8  24  28   0   0  16  28
%e A061858    8  |  0   0   0   0   0   0   0   0   0   0   0   0
%e A061858    9  |  0   0   0   0   0   0   0   0   0  16   0  16
%e A061858   10  |  0   0   0   0   0  16   0  16   0   0  32  32
%e A061858   11  |  0   0   0   4   0  16   8  28   0  16  32  52
%e A061858 (End)
%Y A061858 "Zoomed in" variant: A061859.
%Y A061858 Rows/columns 3, 5 and 7 are given by A048728, A048729, A048730.
%Y A061858 Main diagonal divided by 4: A213673.
%Y A061858 Numbers that generate no carries when multiplied in binary by 11_2: A003714, by 101_2: A048716, by 1001_2: A115845, by 10001_2: A115847, by 100001_2: A114086.
%Y A061858 Other sequences related to the presence/absence of a carry in binary multiplication: A116361, A235034, A235040, A236378, A266195, A289726.
%K A061858 nonn,tabl,easy
%O A061858 0,25
%A A061858 _Antti Karttunen_, May 11 2001