A029750 List of numbers of the form 2^k times 1, 3, 5 or 7.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 20, 24, 28, 32, 40, 48, 56, 64, 80, 96, 112, 128, 160, 192, 224, 256, 320, 384, 448, 512, 640, 768, 896, 1024, 1280, 1536, 1792, 2048, 2560, 3072, 3584, 4096, 5120, 6144, 7168, 8192, 10240

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2).

Programs

Mathematica

CoefficientList[Series[-(x + 1)^2 (x^2 + 1)^2/(2 x^4 - 1), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 19 2013 *)
LinearRecurrence[{0,0,0,2},{1,2,3,4,5,6,7},50] (* Harvey P. Dale, Aug 24 2019 *)

PARI

a(n)=if(n<9,n,[4,5,6,7][n%4+1]<<(n\4-1)) \\ Charles R Greathouse IV, Feb 18 2013

Formula

a(n) = 2a(n-4) for n > 7. - Charles R Greathouse IV, Feb 18 2013

G.f.: -x*(x+1)^2*(x^2+1)^2 / (2*x^4-1). - Colin Barker, Jul 19 2013

Sum_{n>=1} 1/a(n) = 352/105. - Amiram Eldar, Feb 18 2021

Extensions

More terms from Colin Barker, Jul 19 2013