A029748 Numbers of the form 2^k times 1, 3 or 7.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 24, 28, 32, 48, 56, 64, 96, 112, 128, 192, 224, 256, 384, 448, 512, 768, 896, 1024, 1536, 1792, 2048, 3072, 3584, 4096, 6144, 7168, 8192, 12288, 14336, 16384, 24576, 28672, 32768, 49152, 57344, 65536, 98304, 114688, 131072

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2).

Crossrefs

Cf. A000079, A005009, A007283, A029744, A029746.

Programs

Mathematica

CoefficientList[Series[-(x^5 + 2 x^4 + 2 x^3 + 3 x^2 + 2 x + 1)/(2 x^3 - 1), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 18 2013 *)
Sort[Flatten[#{1,3,7}&/@(2^Range[0,20])]] (* Harvey P. Dale, Jan 30 2014 *)

Formula

From Colin Barker, Jul 19 2013: (Start)

a(n) = 2*a(n-3) for n>5.

G.f.: -(x^5+2*x^4+2*x^3+3*x^2+2*x+1) / (2*x^3-1). (End)

Sum_{n>=0} 1/a(n) = 62/21. - Amiram Eldar, Jan 17 2022

Extensions

More terms from Colin Barker, Jul 19 2013