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 A080100 a(n) = 2^(number of 0's in binary representation of n). 15
 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; text; internal format)
 OFFSET 0,3 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. Same parity as the Catalan numbers (A000108). - Paul D. Hanna, Nov 14 2012 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..8191 R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences, arXiv:math/0307027 [math.CO], 2003. FORMULA 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) = 2^A080791(n). a(n)=2^A023416(n), n>0. a(n) = sum(k=0, n, C(n+k, k) mod 2). - Benoit Cloitre, Mar 06 2004 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 MATHEMATICA f[n_] := 2^DigitCount[n, 2, 0]; f[0] = 1; Array[f, 94, 0] (* Robert G. Wilson v *) 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) import Data.List (transpose) a080100 n = a080100_list !! n a080100_list =  1 : zs where    zs =  1 : (concat \$ transpose [map (* 2) zs, zs]) -- Reinhard Zumkeller, Aug 27 2014, Mar 07 2011 CROSSREFS Cf. A001316. Cf. A002487. This is Guy Steele's sequence GS(5, 3) (see A135416). Cf. A048896. Sequence in context: A109090 A220780 A323915 * A161822 A001176 A136693 Adjacent sequences:  A080097 A080098 A080099 * A080101 A080102 A080103 KEYWORD nonn,base AUTHOR Reinhard Zumkeller, Jan 28 2003 EXTENSIONS Keyword base added by Rémy Sigrist, Jan 18 2018 STATUS approved

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Last modified February 25 07:33 EST 2020. Contains 332221 sequences. (Running on oeis4.)