A099899 Multiplies by 4 and shifts right under the XOR BINOMIAL transform (A099898).

1, 5, 21, 69, 277, 1349, 5141, 16453, 65813, 329029, 1381397, 4538437, 18088213, 88081733, 335549461, 1073758277, 4295033109, 21475165509, 90195694613, 296357281861, 1189724029205, 5793998964037, 22080762418197, 70666170679365

Offset

0,2

Comments

Equals the XOR BINOMIAL transform of A099898. Also, equals the main diagonal of the XOR difference triangle A099897, in which the central terms of the rows form the powers of 4. See A099884 for the definitions of XOR difference triangle and the XOR BINOMIAL transform.

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = SumXOR_{k=0..n} (C(n-k+[k/2], [k/2])mod 2)*2^k for n>=0. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A099898(n-i), where SumXOR is the analog of summation under the binary XOR operation and C(i, j)mod 2 = A047999(i, j).

Prog

(PARI) {a(n)=local(B); B=0; for(k=0, n, B=bitxor(B, binomial(n-k+k\2, k\2)%2*4^k)); B}

Crossrefs

Cf. A099884, A099897, A099898.

Sequence in context: A271282 A203287 A296720 * A269566 A271492 A202462

Adjacent sequences: A099896 A099897 A099898 * A099900 A099901 A099902

Keyword

nonn

Author

Paul D. Hanna, Oct 30 2004

Status

approved