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A068052
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Start from 1, shift one left and sum mod 2 (bitwise-XOR) to get 3 (11 in binary), then shift two steps left and XOR to get 15 (1111 in binary), then three steps and XOR to get 119 (1110111 in binary), then four steps and so on.
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10
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1, 3, 15, 119, 1799, 59367, 3743271, 481693095, 123123509927, 62989418816679, 64491023022979239, 132015402419352060071, 540829047855347718631591, 4430403202865824763042320551, 72583450474242118015031400337575, 2378466805556971511916001231449723047
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OFFSET
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0,2
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COMMENTS
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a(n) = each row of A053632 reduced mod 2 and interpreted as a binary number.
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LINKS
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FORMULA
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a(0) = 1; for n > 0, a(n) = a(n-1) XOR (2^n)*a(n-1), where XOR is bitwise-XOR (A003987).
A000120(a(n)) = A285103(n). [Number of ones in binary representation.]
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MAPLE
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with(gfun, seriestolist); [seq(foo(map(`mod`, seriestolist(series(mul(1+(z^i), i=1..n), z, binomial(n+1, 2)+1)), 2)), n=0..20)];
foo := proc(a) local i; add(a[i]*2^(i-1), i=1..nops(a)); end;
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1,
(t-> Bits[Xor](2^n*t, t))(a(n-1)))
end:
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MATHEMATICA
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FoldList[BitXor[#, #*#2]&, 1, 2^Range[20]] (* Paolo Xausa, Mar 07 2024 *)
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PROG
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(Scheme, with memoization-macro definec)
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CROSSREFS
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Same sequence shown in binary: A068053.
Cf. A000120, A003987, A028362 (using + instead of XOR), A048675, A053632, A080791, A248663, A285101, A285102, A285103, A285105.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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