The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A224520 Numbers a(n) with property a(n) + a(n+4) = 2^(n+4) - 1 = A000225(n+4). 2

%I #31 Aug 23 2021 14:01:29

%S 0,1,3,7,15,30,60,120,240,481,963,1927,3855,7710,15420,30840,61680,

%T 123361,246723,493447,986895,1973790,3947580,7895160,15790320,

%U 31580641,63161283,126322567,252645135,505290270,1010580540

%N Numbers a(n) with property a(n) + a(n+4) = 2^(n+4) - 1 = A000225(n+4).

%C This is the case k=4 of a(n) + a(n+k) = 2^(n+k) - 1 = A000225(n+k). The sequences A000975, A077854 and A153234 correspond to cases k=1,2 and 3, respectively.

%H G. C. Greubel, <a href="/A224520/b224520.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,-1,3,-2).

%F a(n) + a(n+4) = 2^(n+4) - 1.

%F From _Joerg Arndt_, Apr 09 2013: (Start)

%F G.f.: x/((1-x)*(1-2*x)*(1+x^4)).

%F a(n) = +3*a(n-1) -2*a(n-2) -1*a(n-4) +3*a(n-5) -2*a(n-6). (End)

%F a(n) = floor(2^(n+4)/17). - _Karl V. Keller, Jr._, Jun 30 2021

%t CoefficientList[Series[x/((1 - x)*(1 - 2*x)*(1 + x^4)), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 11 2017 *)

%t LinearRecurrence[{3,-2,0,-1,3,-2},{0,1,3,7,15,30},40] (* _Harvey P. Dale_, Aug 23 2021 *)

%o (PARI) x='x+O('x^50); concat([0], Vec(x/((1-x)*(1-2*x)*(1+x^4)))) \\ _G. C. Greubel_, Oct 11 2017

%o (Python) print([2**(n+4)//17 for n in range(31)]) # _Karl V. Keller, Jr._, Jun 30 2021

%Y Cf. A000975, A077854, A153234.

%K nonn,easy

%O 0,3

%A _Arie Bos_, Apr 09 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 6 13:43 EDT 2024. Contains 373128 sequences. (Running on oeis4.)