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A080100
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2^(number of 0's in binary representation of n).
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7
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences
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FORMULA
| G.f. satisfies F(x^2) = (1+F(x))/(x+2). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 28 2003
a(2n) = 2a(n), n>0. a(2n+1) = a(n). - Ralf Stephan, Apr 29 2003
a(n)=2^A080791(n). a(n)=2^A023416(n), n>0.
a(n)=sum(k=0, n, C(n+k, k) mod 2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 06 2004
a(n)=sum(k=0, n, C(2n-k, n) mod 2) - Paul Barry (pbarry(AT)wit.ie), Dec 13 2004
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MATHEMATICA
| f[n_] := 2^DigitCount[n, 2, 0]; f[0] = 1; Array[f, 94, 0] (* RGWv *)
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PROG
| (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)
a080100 n = a080100_list !! n
a080100_list = 1 : f [1] where f (x:xs) = x : f (xs ++ [2*x, x])
-- Reinhard Zumkeller, Mar 07 2011
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CROSSREFS
| Cf. A001316.
Cf. A002487.
This is Guy Steele's sequence GS(5, 3) (see A135416).
Sequence in context: A145983 A120025 A109090 * A161822 A001176 A136693
Adjacent sequences: A080097 A080098 A080099 * A080101 A080102 A080103
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 28 2003
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