A061858 - OEIS

%I #13 Feb 14 2021 13:16:33

%S 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 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 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 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 a(n) = A004247(n) - A048720(n).

%e From _Peter Munn_, Jan 28 2021: (Start)

%e The top left 12 X 12 corner of the table:

%e       |  0   1   2   3   4   5   6   7   8   9  10  11

%e ------+------------------------------------------------

%e    0  |  0   0   0   0   0   0   0   0   0   0   0   0

%e    1  |  0   0   0   0   0   0   0   0   0   0   0   0

%e    2  |  0   0   0   0   0   0   0   0   0   0   0   0

%e    3  |  0   0   0   4   0   0   8  12   0   0   0   4

%e    4  |  0   0   0   0   0   0   0   0   0   0   0   0

%e    5  |  0   0   0   0   0   8   0   8   0   0  16  16

%e    6  |  0   0   0   8   0   0  16  24   0   0   0   8

%e    7  |  0   0   0  12   0   8  24  28   0   0  16  28

%e    8  |  0   0   0   0   0   0   0   0   0   0   0   0

%e    9  |  0   0   0   0   0   0   0   0   0  16   0  16

%e   10  |  0   0   0   0   0  16   0  16   0   0  32  32

%e   11  |  0   0   0   4   0  16   8  28   0  16  32  52

%e (End)

%Y "Zoomed in" variant: A061859.

%Y Rows/columns 3, 5 and 7 are given by A048728, A048729, A048730.

%Y Main diagonal divided by 4: A213673.

%Y 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 Other sequences related to the presence/absence of a carry in binary multiplication: A116361, A235034, A235040, A236378, A266195, A289726.

%K nonn,tabl,easy

%O 0,25

%A _Antti Karttunen_, May 11 2001