A004134 Denominators in expansion of (1-x)^{-1/4} are 2^a(n).

0, 2, 5, 7, 11, 13, 16, 18, 23, 25, 28, 30, 34, 36, 39, 41, 47, 49, 52, 54, 58, 60, 63, 65, 70, 72, 75, 77, 81, 83, 86, 88, 95, 97, 100, 102, 106, 108, 111, 113, 118, 120, 123, 125, 129, 131, 134, 136, 142, 144, 147, 149, 153, 155, 158, 160, 165, 167, 170, 172, 176, 178

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• R. Stephan, Some divide-and-conquer sequences ...
• R. Stephan, Table of generating functions

Crossrefs

Cf. A004130.

Cf. A005187.

Programs

Mathematica

Log2[ Denominator[ CoefficientList[ Series[ 1/Sqrt[Sqrt[1 - x]], {x, 0, 61}], x]]] (* Robert G. Wilson v, Mar 23 2014 *)
f[n_] := 3 n - DigitCount[n, 2, 1]; Array[f, 62, 0] (* or *)
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 *)

PARI

{a(n) = if( n<0, 0, 3*n - subst( Pol( binary( n ) ), x, 1) ) } /* Michael Somos, Aug 23 2007 */

PARI

a(n) = 3*n - hammingweight(n); \\ Joerg Arndt, Mar 23 2014

Formula

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.

a(n) = A005187(n) + n. - Cyril Damamme, Aug 04 2015