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A048723
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Binary "exponentiation" without carries: {0..y}^{0..x}, where y (column index) is binary encoding of GF(2)-polynomial and x (row index) is the exponent.
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17
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1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 4, 3, 1, 0, 1, 8, 5, 4, 1, 0, 1, 16, 15, 16, 5, 1, 0, 1, 32, 17, 64, 17, 6, 1, 0, 1, 64, 51, 256, 85, 20, 7, 1, 0, 1, 128, 85, 1024, 257, 120, 21, 8, 1, 0, 1, 256, 255, 4096, 1285, 272, 107, 64, 9, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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FORMULA
| a(n) = Xpower( (n-((trinv(n)*(trinv(n)-1))/2)), (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) );
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EXAMPLE
| 1 0 0 0 0 0 0 0 0 ...
1 1 1 1 1 1 1 1 1 ...
1 2 4 8 16 32 64 128 256 ...
1 3 5 15 17 51 85 255 257 ...
1 4 16 64 256 1024 4096 16384 65536 ...
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MAPLE
| # Xmult and trinv have been given in A048720.
Xpower := proc(nn, mm) option remember; if(0 = mm) then RETURN(1); # By definition, also 0^0 = 1. else RETURN(Xmult(nn, Xpower(nn, mm-1))); fi; end;
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CROSSREFS
| Cf. ordinary power table A004248 and A034369, A034373.
Cf. A048710. Row 3: A001317, Row 5: A038183 (bisection of row 3), Row 7: A038184. Column 2: A000695, diagonal of A048720. Diagonal: A048731.
Sequence in context: A055340 A119328 A058716 * A088455 A004248 A034373
Adjacent sequences: A048720 A048721 A048722 * A048724 A048725 A048726
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KEYWORD
| nonn,tabl
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AUTHOR
| Antti Karttunen, Apr 26 1999
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