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Search: id:A099885
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| A099885 |
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Central terms of the rows of the XOR difference triangle of the powers of 2 (A099884) so that a(n) = A099884(n,[n/2]). |
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+0
2
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| 1, 2, 6, 12, 20, 40, 120, 240, 272, 544, 1632, 3264, 5440, 10880, 32640, 65280, 65792, 131584, 394752, 789504, 1315840, 2631680, 7895040, 15790080, 17895424, 35790848, 107372544, 214745088, 357908480, 715816960, 2147450880, 4294901760
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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XOR BINOMIAL transform of this sequence is A099886.
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FORMULA
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a(n) = 2^[(n+1)/2]*A001317([n/2]), where A001317 forms the XOR BINOMIAL transform of the powers of 2.
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EXAMPLE
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XOR difference triangle of the powers of 2 (A099884) begins:
[_1],
[_2,3],
[4,_6,5],
[8,_12,10,15],
[16,24,_20,30,17],
[32,48,_40,60,34,51],
[64,96,80,_120,68,102,85],
[128,192,160,_240,136,204,170,255],...
(the central terms are underscored).
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PROGRAM
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(PARI) {a(n)=local(B); B=0; for(i=0, n\2, B=bitxor(B, binomial(n\2, i)%2*2^(n\2-i))); 2^((n+1)\2)*B}
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CROSSREFS
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Cf. A099884, A001317, A099886.
Sequence in context: A078878 A095361 A095362 this_sequence A106372 A022450 A011892
Adjacent sequences: A099882 A099883 A099884 this_sequence A099886 A099887 A099888
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2004
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