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

Author

Paul D. Hanna, Oct 30 2004

Keywords

• nonn

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.

Crossrefs

Cf. A099884, A099897, A099899.

Programs

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}

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).