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 A099898 Shifts left and divides by 4 under the XOR BINOMIAL transform (A099899). 2
 1, 4, 20, 84, 276, 1108, 5396, 20564, 65812, 263252, 1316116, 5525588, 18153748, 72352852, 352326932, 1342197844, 4295033108, 17180132436, 85900662036, 360782778452, 1185429127444, 4758896116820, 23175995856148, 88323049672788 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified April 22 14:33 EDT 2019. Contains 322356 sequences. (Running on oeis4.)