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 A004134 Denominators in expansion of (1-x)^{-1/4} are 2^a(n). 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 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 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 *) PROG (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 CROSSREFS Cf. A004130. Cf. A005187. Sequence in context: A243047 A113543 A189468 * A191406 A322969 A229470 Adjacent sequences:  A004131 A004132 A004133 * A004135 A004136 A004137 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 16 08:30 EDT 2021. Contains 347469 sequences. (Running on oeis4.)