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A029750 List of numbers of the form 2^k times 1, 3, 5 or 7. 20

%I #26 Feb 18 2021 03:03:05

%S 1,2,3,4,5,6,7,8,10,12,14,16,20,24,28,32,40,48,56,64,80,96,112,128,

%T 160,192,224,256,320,384,448,512,640,768,896,1024,1280,1536,1792,2048,

%U 2560,3072,3584,4096,5120,6144,7168,8192,10240

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

%H Vincenzo Librandi, <a href="/A029750/b029750.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2).

%F a(n) = 2a(n-4) for n > 7. - _Charles R Greathouse IV_, Feb 18 2013

%F G.f.: -x*(x+1)^2*(x^2+1)^2 / (2*x^4-1). - _Colin Barker_, Jul 19 2013

%F Sum_{n>=1} 1/a(n) = 352/105. - _Amiram Eldar_, Feb 18 2021

%t CoefficientList[Series[-(x + 1)^2 (x^2 + 1)^2/(2 x^4 - 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 19 2013 *)

%t LinearRecurrence[{0,0,0,2},{1,2,3,4,5,6,7},50] (* _Harvey P. Dale_, Aug 24 2019 *)

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

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Jul 19 2013

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)