A099901 Shifts left and divides by 2 under the XOR BINOMIAL transform (A099902).

1, 2, 6, 14, 22, 46, 118, 206, 278, 558, 1654, 3790, 5910, 11310, 28790, 49358, 65814, 131630, 394870, 921294, 1447702, 3025966, 7762038, 13549774, 18284822, 36438574, 108004982, 247467726, 385881878, 738208814, 1879076982, 3221274830

Offset

0,2

Comments

Equals the XOR BINOMIAL transform of A099902. Also, equals the leftmost column of the XOR difference triangle A099900, in which the central terms of the rows forms the powers of 2.

Links

Table of n, a(n) for n=0..31.

Formula

a(0)=1; a(n) = SumXOR_{k=0..n-1} (C(n-1-k+[k/2], [k/2])mod 2)*2^(k+1) for n>0. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A099902(n-i), where SumXOR is the analog of summation under the binary XOR operation and C(k, i)mod 2 = A047999(k, i).

Prog

(PARI) {a(n)=local(B); B=0; if(n==0, B=1, for(k=0, n-1, B=bitxor(B, binomial(n-1-k+k\2, k\2)%2*2^(k+1)))); B}

Crossrefs

Cf. A099884, A099900, A099902.

Sequence in context: A172304 A160164 A074729 * A119846 A119844 A016060

Adjacent sequences: A099898 A099899 A099900 * A099902 A099903 A099904

Keyword

eigen,nonn

Author

Paul D. Hanna, Oct 30 2004

Status

approved