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%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
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