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 A094780 Let 2^k = smallest power of 2 >= binomial(2n,n); a(n) = 2^k - binomial(2n,n). 2

%I

%S 0,0,2,12,58,4,100,664,3514,16916,77388,343144,1490148,6376616,

%T 26992264,113317936,472661434,1961361076,8104733884,33374212936,

%U 137031378124,11497939448,94924291832,562662294608,2936768405732,14326881917576,67031420473208,304860388037136

%N Let 2^k = smallest power of 2 >= binomial(2n,n); a(n) = 2^k - binomial(2n,n).

%C Suggested by reading the Knuth article.

%D D. E. Knuth, Efficient balanced codes, IEEE Trans. Inform. Theory, 32 (No. 1, 1986), 51-53.

%e C(30,15) = 155117520; 2^28 = 268435456; difference is 113317936.

%e k = 0, 1, 3, 5, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, ... - _R. J. Mathar_, Nov 15 2019

%p A094780 := proc(n)

%p local cb,k ;

%p cb := binomial(2*n,n) ;

%p k := ceil(log[2](cb)) ;

%p 2^k-cb ;

%p end proc:

%p seq(A094780(n),n=0..10); # _R. J. Mathar_, Nov 15 2019

%Y Cf. A093387, A094779.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jun 10 2004

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Last modified February 17 12:07 EST 2020. Contains 331996 sequences. (Running on oeis4.)