Search: id:A000630
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%I A000630
%S A000630 1,1,2,3,7,12,23,41,81,149,282,522,987,1843,3463,6473,12160,22773,42719,
%T A000630 80025,150074,281258,527320,988334,1852849,3473061,6510681,12204139,
%U A000630 22877649,42884585,80389797,150692973,282481747,529522496,992614937
%N A000630 Number of ways to represent n using the binary operator a * b = 2^a + 
               b.
%D A000630 D. E. Knuth, personal communication.
%F A000630 Sum a(n) q^n = (1 - Sum a(n) q^(2^n ) )^-1.
%F A000630 As n increases, a(n+1)/a(n) approaches a value x = 1.874542... satisfying 
               1 = ( Sum a(j)/x^(2^j), j >= 0 ) [ David W. Wilson ].
%e A000630 E.g. 4=1+1+1+1=2^1 + 1+1=2^1 +2^1 =2^2 = 2^1+1 =1+2^1 + 1=1+1+2^1.
%Y A000630 Sequence in context: A056179 A027675 A054176 this_sequence A036538 A108742 
               A018240
%Y A000630 Adjacent sequences: A000627 A000628 A000629 this_sequence A000631 A000632 
               A000633
%K A000630 nonn,easy,nice
%O A000630 0,3
%A A000630 N. J. A. Sloane (njas(AT)research.att.com).
%E A000630 More terms from David W. Wilson (davidwwilson(AT)comcast.net)

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