cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A163227 Fibonacci-accumulation sequence.

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%I A163227 #11 Aug 20 2025 19:34:40
%S A163227 1,1,1,2,2,4,3,7,5,12,8,20,13,33,21,54,34,88,55,143,89,232,144,376,
%T A163227 233,609,377,986,610,1596,987,2583,1597,4180,2584,6764,4181,10945,
%U A163227 6765,17710,10946,28656,17711,46367,28657,75024,46368,121392,75025,196417
%N A163227 Fibonacci-accumulation sequence.
%C A163227 Accumulation of A000045 and A000071.
%H A163227 G. C. Greubel, <a href="/A163227/b163227.txt">Table of n, a(n) for n = 1..1000</a>
%H A163227 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,0,0,-1).
%F A163227 a(n) = 2*a(n-2) - a(n-6), where a(1,2,3)=1.
%F A163227 G.f.: x*(1 + x - x^2)/(1 - 2*x^2 + x^6). - _G. C. Greubel_, Dec 11 2016
%t A163227 LinearRecurrence[{0, 2, 0, 0, 0, -1}, {1, 1, 1, 2, 2, 4}, 50] (* or *) CoefficientList[Series[x*(1 + x - x^2)/(1 - 2*x^2 + x^6), {x,1,50}], x] (* _G. C. Greubel_, Dec 11 2016 *)
%o A163227 (PARI) Vec(x*(1 + x - x^2)/(1 - 2*x^2 + x^6) + O(x^50)) \\ _G. C. Greubel_, Dec 11 2016
%o A163227 (Magma) m:=55; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x-x^2)/(1-2*x^2+x^6))); // _Vincenzo Librandi_, Dec 12 2016
%Y A163227 Cf. A000071, A000045, A097110.
%K A163227 nonn,easy
%O A163227 1,4
%A A163227 _Mark Dols_, Jul 23 2009