1,1

Nonzero terms form A101121 and occur at positions 2^k for k>=0. A101119 equals the nonzero differences of A006519 and A003484. See A099884 for the definition of the XOR BINOMIAL transform.

a(n) = SumXOR_{k=0..n} (C(n, k)Mod2)*A101119(k), where SumXOR is summation under XOR. A101119(n) = SumXOR_{k=0..n} (C(n, k)Mod2)*a(k). a(2^(n-1)) = A101121(n) for n>=1, and a(k)=0 when k is not a power of 2.

(PARI) {a(n)=local(B); B=0; for(i=0, n-1, B=bitxor(B, binomial(n-1, i)%2* (16*2^valuation(n-i, 2)-2^(valuation(n-i, 2)%4)-8*(valuation(n-i, 2)\4)-8))); B}

Cf. A003484, A006519, A101119, A101120, A101121.

Sequence in context: A056613 A029498 A129422 this_sequence A090535 A107778 A122735

Adjacent sequences: A101119 A101120 A101121 this_sequence A101123 A101124 A101125

nonn

Simon Plouffe (simon.plouffe(AT)gmail.com) and Paul D. Hanna (pauldhanna(AT)juno.com), Dec 02 2004