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 A277561 a(n) = Sum_{k=0..n} ({binomial(n+2k,2k)*binomial(n,k)} mod 2). 5
 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 4, 2, 4, 2, 2, 2, 4, 4, 4, 4, 8, 4, 4, 2, 4, 4, 4, 2, 4, 2, 2, 2, 4, 4, 4, 4, 8, 4, 4, 4, 8, 8, 8, 4, 8, 4, 4, 2, 4, 4, 4, 4, 8, 4, 4, 2, 4, 4, 4, 2, 4, 2, 2, 2, 4, 4, 4, 4, 8, 4, 4, 4, 8, 8, 8, 4, 8, 4, 4, 4, 8, 8, 8, 8, 16, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equals the run length transform of A040000: 1,2,2,2,2,2,... LINKS Chai Wah Wu, Table of n, a(n) for n = 0..10000 Chai Wah Wu, Sums of products of binomial coefficients mod 2 and run length transforms of sequences, arXiv:1610.06166 [math.CO], 2016. FORMULA a(n) = 2^A069010(n). a(2n) = a(n), a(4n+1) = 2a(n), a(4n+3) = a(2n+1). - Chai Wah Wu, Nov 04 2016 a(n) = A034444(A005940(1+n)). - Antti Karttunen, May 29 2017 MATHEMATICA Table[Sum[Mod[Binomial[n + 2 k, 2 k] Binomial[n, k], 2], {k, 0, n}], {n, 0, 86}] (* Michael De Vlieger, Oct 21 2016 *) PROG (Python) def A277561(n):     return sum(int(not (~(n+2*k) & 2*k) | (~n & k)) for k in range(n+1)) (PARI) a(n) = sum(k=0, n, binomial(n+2*k, 2*k)*binomial(n, k) % 2); \\ Michel Marcus, Oct 21 2016 CROSSREFS Cf. A005940, A034444, A040000, A069010, A106737. Sequence in context: A183095 A304817 A242802 * A317684 A127973 A300654 Adjacent sequences:  A277558 A277559 A277560 * A277562 A277563 A277564 KEYWORD nonn AUTHOR Chai Wah Wu, Oct 19 2016 STATUS approved

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Last modified November 18 17:49 EST 2018. Contains 317323 sequences. (Running on oeis4.)