A099886 - OEIS

%I #10 Jul 13 2015 23:52:46

%S 1,3,7,9,21,63,107,189,273,819,1911,2457,5189,15567,28123,46701,65793,

%T 197379,460551,592137,1381653,4144959,7039851,12434877,17829905,

%U 53489715,124809335,160469145,340873541,1022620623,1840690907

%N XOR binomial transform of A099885.

%C 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).

%F 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 analog of summation under XOR and x\y stands for floor(x/y) (see Pari program).

%o (PARI) {a(n)=my(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}

%Y Cf. A099884, A001317, A099885.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 28 2004