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

0,2

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).

Links

Table of n, a(n) for n=0..30.

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).

Prog

(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}

Crossrefs

Cf. A099884, A001317, A099885.

Sequence in context: A018458 A029539 A018267 * A118564 A098338 A033958

Adjacent sequences: A099883 A099884 A099885 * A099887 A099888 A099889

Keyword

nonn

Author

Paul D. Hanna, Oct 28 2004

Status

approved