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%I #61 Feb 08 2024 07:12:35
%S 3,12,51,204,819,3276,13107,52428,209715,838860,3355443,13421772,
%T 53687091,214748364,858993459,3435973836,13743895347,54975581388,
%U 219902325555,879609302220,3518437208883,14073748835532,56294995342131,225179981368524,900719925474099
%N Every run length in base 2 is 2.
%C a(n) is the number whose binary representation is A153435(n). - _Omar E. Pol_, Jan 18 2009
%C See A033001 and following for the analog in other bases and the variant with runs of length >= 2. - _M. F. Hasler_, Feb 01 2014
%H Vincenzo Librandi, <a href="/A043291/b043291.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,1,-4).
%F a(n) = 4*a(n-1)+a(n-2)-4*a(n-3), n>3. - _John W. Layman_, Feb 01 2000
%F a(n) = floor(4^(n+1)/5). - _Mircea Merca_, Dec 26 2010
%F G.f.: 3*x / ( (x-1)*(4*x-1)*(1+x) ). - _Joerg Arndt_, Jan 08 2011
%F a(n) = 3*A033114(n). - _R. J. Mathar_, Jan 08 2011
%p seq(floor(4^(n+1)/5),n=1..25); # _Mircea Merca_, Dec 26 2010
%t f[n_] := Floor[4^(n + 1)/5]; Array[f, 23] (* or *)
%t a[1] = 3; a[2] = 12; a[3] = 51; a[n_] := a[n] = 4 a[n - 1] + a[n - 2] - 4 a[n - 3]; Array[a, 23] (* or *)
%t 3 LinearRecurrence[{4, 1, -4}, {1, 4, 17}, 23] (* _Robert G. Wilson v_, Jul 01 2014 *)
%o (Magma) [Floor(4^(n+1)/5): n in [1..30]]; // _Vincenzo Librandi_, Jun 26 2011
%o (PARI) A043291 = n->4^(n+1)\5 \\ _M. F. Hasler_, Feb 01 2014
%o (Python)
%o def a(n): return int(''.join([['11', '00'][i%2] for i in range(n)]), 2)
%o print([a(n) for n in range(1, 26)]) # _Michael S. Branicky_, Mar 12 2021
%Y Cf. A153435 (binary).
%Y Bisections: A108020, A182512. Bisection of A077854.
%Y Cf. A000975, A033001, A033114.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_
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