|
%I #26 Aug 04 2015 03:49:30
%S 0,2,5,7,11,13,16,18,23,25,28,30,34,36,39,41,47,49,52,54,58,60,63,65,
%T 70,72,75,77,81,83,86,88,95,97,100,102,106,108,111,113,118,120,123,
%U 125,129,131,134,136,142,144,147,149,153,155,158,160,165,167,170,172,176,178
%N Denominators in expansion of (1-x)^{-1/4} are 2^a(n).
%H Vincenzo Librandi, <a href="/A004134/b004134.txt">Table of n, a(n) for n = 0..1000</a>
%H R. Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H R. Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%F a(n) = 3*n - A000120(n). Recurrence: a(2n) = a(n) + 3n, a(2n+1) = a(n) + 3n + 2. Proved by _Mitch Harris_, following a conjecture by _Ralf Stephan_.
%F a(n) = A005187(n) + n. - _Cyril Damamme_, Aug 04 2015
%t Log2[ Denominator[ CoefficientList[ Series[ 1/Sqrt[Sqrt[1 - x]], {x, 0, 61}], x]]] (* _Robert G. Wilson v_, Mar 23 2014 *)
%t f[n_] := 3 n - DigitCount[n, 2, 1]; Array[f, 62, 0] (* or *)
%t a[n_] := If[ OddQ@ n, a[(n - 1)/2] + 3 (n - 1)/2 + 2, a[n/2] + 3 n/2]; a[0] = 0; Array[a, 62, 0] (* _Robert G. Wilson v_, Mar 23 2014 *)
%o (PARI) {a(n) = if( n<0, 0, 3*n - subst( Pol( binary( n ) ), x, 1) ) } /* _Michael Somos_, Aug 23 2007 */
%o (PARI) a(n) = 3*n - hammingweight(n); \\ _Joerg Arndt_, Mar 23 2014
%Y Cf. A004130.
%Y Cf. A005187.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
|
