A099898 Shifts left and divides by 4 under the XOR BINOMIAL transform (A099899).

1, 4, 20, 84, 276, 1108, 5396, 20564, 65812, 263252, 1316116, 5525588, 18153748, 72352852, 352326932, 1342197844, 4295033108, 17180132436, 85900662036, 360782778452, 1185429127444, 4758896116820, 23175995856148, 88323049672788

Offset

0,2

Comments

Equals the XOR BINOMIAL transform of A099899. Also, equals the leftmost column of the XOR difference triangle A099897, in which the central terms of the rows forms 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(0)=1; a(n) = SumXOR_{k=0..n-1} (C(n-1-k+[k/2], [k/2])mod 2)*4^(k+1) for n>0. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A099899(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*4^(k+1)))); B}

Crossrefs

Cf. A099884, A099897, A099899.

Sequence in context: A055296 A140532 A217482 * A003489 A167682 A246574

Adjacent sequences: A099895 A099896 A099897 * A099899 A099900 A099901

Keyword

nonn

Author

Paul D. Hanna, Oct 30 2004

Status

approved