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Gould's sequence A001316 in binary.
0

%I #10 Jan 12 2024 00:52:56

%S 1,10,10,100,10,100,100,1000,10,100,100,1000,100,1000,1000,10000,10,

%T 100,100,1000,100,1000,1000,10000,100,1000,1000,10000,1000,10000,

%U 10000,100000,10,100,100,1000,100,1000,1000,10000,100,1000,1000,10000,1000

%N Gould's sequence A001316 in binary.

%F Formulas due to Paul D. Hanna:

%F a(n) = 10^A000120(n).

%F a(n) = Product_{k=0..log_2(n)} 10^b(n,k) where b(n,k) = coefficient of 2^k in binary expansion of n.

%F a(n) = Sum_{k=0..n} (C(n,k) mod 2)*9^A000120(n-k).

%F G.f.: Product_{k>=0} 1 + 10*x^(2^k).

%o (PARI) a(n) = 10^hammingweight(n); \\ _Kevin Ryde_, Jan 11 2024

%Y Cf. A001316, A048883, A102376.

%K easy,base,nonn

%O 0,2

%A _Paul Barry_, Jan 05 2005