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 A099901 Shifts left and divides by 2 under the XOR BINOMIAL transform (A099902). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 5 19:22 EDT 2021. Contains 343573 sequences. (Running on oeis4.)