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Search: id:A099886
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| 1, 3, 7, 9, 21, 63, 107, 189, 273, 819, 1911, 2457, 5189, 15567, 28123, 46701, 65793, 197379, 460551, 592137, 1381653, 4144959, 7039851, 12434877, 17829905, 53489715, 124809335, 160469145, 340873541, 1022620623, 1840690907
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OFFSET
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0,2
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COMMENT
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Many terms of this sequence are equal to 3 times another term! Why? The XOR BINOMIAL transform of this sequence is A099885. A099885 is the central terms of the rows of the XOR difference triangle of the powers of 2 (A099884).
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FORMULA
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a(n) = SumXOR_{k=0..n} SumXOR_{i=0..k\2} (C(n, k)mod 2)*(C(k\2, i)mod 2)*2^((k+1)\2+k\2-i), where the SumXOR is the analogue of summation under XOR.
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PROGRAM
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(PARI) {a(n)=local(B); B=0; for(k=0, n, for(i=0, k\2, B=bitxor(B, binomial(n, k)%2*binomial(k\2, i)%2*2^((k+1)\2+k\2-i) ))); B}
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CROSSREFS
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Cf. A099884, A001317, A099885.
Sequence in context: A018458 A029539 A018267 this_sequence A118564 A098338 A033958
Adjacent sequences: A099883 A099884 A099885 this_sequence A099887 A099888 A099889
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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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