

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.


12



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, 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, 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
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OFFSET

0,25


LINKS

Table of n, a(n) for n=0..101.


FORMULA

a(n) = A004247(n)  A048720(n).


EXAMPLE

From Peter Munn, Jan 28 2021: (Start)
The top left 12 X 12 corner of the table:
 0 1 2 3 4 5 6 7 8 9 10 11
+
0  0 0 0 0 0 0 0 0 0 0 0 0
1  0 0 0 0 0 0 0 0 0 0 0 0
2  0 0 0 0 0 0 0 0 0 0 0 0
3  0 0 0 4 0 0 8 12 0 0 0 4
4  0 0 0 0 0 0 0 0 0 0 0 0
5  0 0 0 0 0 8 0 8 0 0 16 16
6  0 0 0 8 0 0 16 24 0 0 0 8
7  0 0 0 12 0 8 24 28 0 0 16 28
8  0 0 0 0 0 0 0 0 0 0 0 0
9  0 0 0 0 0 0 0 0 0 16 0 16
10  0 0 0 0 0 16 0 16 0 0 32 32
11  0 0 0 4 0 16 8 28 0 16 32 52
(End)


CROSSREFS

"Zoomed in" variant: A061859.
Rows/columns 3, 5 and 7 are given by A048728, A048729, A048730.
Main diagonal divided by 4: A213673.
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.
Other sequences related to the presence/absence of a carry in binary multiplication: A116361, A235034, A235040, A236378, A266195, A289726.
Sequence in context: A089418 A274981 A124856 * A005873 A217511 A307380
Adjacent sequences: A061855 A061856 A061857 * A061859 A061860 A061861


KEYWORD

nonn,tabl,easy


AUTHOR

Antti Karttunen, May 11 2001


STATUS

approved



