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.
%I A246075 #17 Sep 25 2017 08:54:51
%S A246075 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18,20,22,24,26,28,32,36,40,44,48,
%T A246075 52,56,64,72,80,88,96,104,112,128,144,160,176,192,208,224,256,288,320,
%U A246075 352,384,416,448,512,576,640,704,768,832,896,1024,1152,1280,1408,1536,1664,1792,2048,2304,2560,2816,3072,3328,3584,4096
%N A246075 Paradigm shift sequence for a (-3,5) production scheme with replacement.
%C A246075 This sequence is the solution to the following problem: "Suppose you have the choice of using one of three production options: apply a simple incremental action, bundle existing output as an integrated product (which requires p=-3 steps), or implement the current bundled action (which requires q=5 steps). The first use of a novel bundle erases (or makes obsolete) all prior actions. How large an output can be generated in n time steps?"
%C A246075 1. A production scheme with replacement R(p,q) eliminates existing output followinging a bundling action, while an additive scheme A(p,q) retains the output. The schemes correspond according to A(p,q)=R(p-q,q), with the replacement scheme serving as the default presentation.
%C A246075 2. This problem is structurally similar to the Copy and Paste Keyboard problem: Existing sequences (A178715 and A193286) should be regarded as Paradigm-Shift Sequences with production schemes R(1,1) and R(2,1) with replacement, respectively.
%C A246075 3. The ideal number of implementations per bundle, as measured by the geometric growth rate (p+zq root of z), is z = 2.
%C A246075 4. All solutions will be of the form a(n) = (qm+r) * m^b * (m+1)^d.
%C A246075 5. For large n, the sequence is recursively defined.
%H A246075 Colin Barker, <a href="/A246075/b246075.txt">Table of n, a(n) for n = 1..1000</a>
%H A246075 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,2).
%F A246075 a(n) = (qd+r) * d^(C-R) * (d+1)^R, where r = (n-Cp) mod q, Q = floor( (R-Cp)/q ), R = Q mod (C+1), and d = floor ( Q/(C+1) ).
%F A246075 a(n) = 2*a(n-7) for all n >= 14.
%F A246075 G.f.: x*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)^2 / (1 -2*x^7). - _Colin Barker_, Nov 18 2016
%t A246075 Join[Range[6], LinearRecurrence[PadLeft[{2}, 7], Range[7, 13], 65]] (* _Jean-François Alcover_, Sep 25 2017 *)
%o A246075 (PARI) Vec(x*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)^2 / (1 -2*x^7) + O(x^100)) \\ _Colin Barker_, Nov 18 2016
%Y A246075 Paradigm shift sequences for implementation size p=5: A103969, A246074, A246075, A246076, A246079, A246083, A246087, A246091, A246095, A246099, A246103.
%Y A246075 Paradigm shift sequences for p<0: A103969, A246074, A246075, A246076, A246079, A029750, A246078, A029747, A246077, A029744, A029747, A131577.
%K A246075 nonn,easy
%O A246075 1,2
%A A246075 _Jonathan T. Rowell_, Aug 13 2014