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

%I #11 Jul 11 2015 01:05:19

%S 1,2,6,14,22,46,118,206,278,558,1654,3790,5910,11310,28790,49358,

%T 65814,131630,394870,921294,1447702,3025966,7762038,13549774,18284822,

%U 36438574,108004982,247467726,385881878,738208814,1879076982,3221274830

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

%C 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.

%F 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).

%o (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}

%Y Cf. A099884, A099900, A099902.

%K eigen,nonn

%O 0,2

%A _Paul D. Hanna_, Oct 30 2004

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)