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A080100
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a(n) = 2^(number of 0's in binary representation of n).
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21
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1, 1, 2, 1, 4, 2, 2, 1, 8, 4, 4, 2, 4, 2, 2, 1, 16, 8, 8, 4, 8, 4, 4, 2, 8, 4, 4, 2, 4, 2, 2, 1, 32, 16, 16, 8, 16, 8, 8, 4, 16, 8, 8, 4, 8, 4, 4, 2, 16, 8, 8, 4, 8, 4, 4, 2, 8, 4, 4, 2, 4, 2, 2, 1, 64, 32, 32, 16, 32, 16, 16, 8, 32, 16, 16, 8, 16, 8, 8, 4, 32, 16, 16, 8, 16, 8, 8, 4, 16, 8, 8, 4, 8, 4
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OFFSET
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0,3
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COMMENTS
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Number of numbers k, 0<=k<=n, such that (k AND n) = 0 (bitwise logical AND): a(n) = #{k : T(n,k)=n, 0<=k<=n}, where T is defined as in A080099.
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LINKS
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FORMULA
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G.f. satisfies: F(x^2) = (1+F(x))/(x+2). - Ralf Stephan, Jun 28 2003
a(2n) = 2a(n), n>0. a(2n+1) = a(n). - Ralf Stephan, Apr 29 2003
a(n) = sum(k=0, n, C(2n-k, n) mod 2). - Paul Barry, Dec 13 2004
G.f. satisfies: A(x) = Sum_{n>=0} [A(x)^n (mod 2)]*x^n, where A(x)^n (mod 2) reduces all coefficients modulo 2 to {0,1}. - Paul D. Hanna, Nov 14 2012
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MATHEMATICA
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PROG
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(PARI) a(n)=if(n<1, n==0, (2-n%2)*a(n\2))
(PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=2; A=subst(A, x, x^2)*(2+x)-1); polcoeff(A, n))
(Haskell)
import Data.List (transpose)
a080100 n = a080100_list !! n
a080100_list = 1 : zs where
zs = 1 : (concat $ transpose [map (* 2) zs, zs])
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CROSSREFS
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This is Guy Steele's sequence GS(5, 3) (see A135416).
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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