A099886 XOR binomial transform of A099885.

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

Offset: 0

Author

Paul D. Hanna, Oct 28 2004

Keywords

• nonn

Comments

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).

Crossrefs

Cf. A099884, A001317, A099885.

Programs

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}

Formula

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).