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.

A253832 a(n) = a(n-1) * (1 + a(n-2)/a(n-4)), a(0) = a(1) = a(2) = a(3) = 1.

This page as a plain text file.
%I A253832 #34 Dec 27 2022 11:37:48
%S A253832 1,1,1,1,2,4,12,60,420,6720,241920,27336960,15773425920,
%T A253832 64182070068480,4184799332605032960,9825130460280752853949440,
%U A253832 2606675287692747620296839987164160,399035505430293222012069797891526139192304640
%N A253832 a(n) = a(n-1) * (1 + a(n-2)/a(n-4)), a(0) = a(1) = a(2) = a(3) = 1.
%C A253832 This sequence is similar to A005831 except for the division.
%H A253832 Seiichi Manyama, <a href="/A253832/b253832.txt">Table of n, a(n) for n = 0..27</a>
%F A253832 0 = a(n)*(a(n+3) - a(n+4)) + a(n+2)*a(n+3) for all n >= 0.
%F A253832 a(n+1) = a(n) * A253853(n) for all n >= 0.
%F A253832 a(n) ~ b * f^(d^n), where b = 0.103038949751108..., f = c^(1/(d-1)) = 2.4130332882212... and d = ((27-3*sqrt(69))/2)^(1/3) / 3 + ((9+sqrt(69))/2)^(1/3) / 3^(2/3) = 1.324717957244746... is the root of the equation d^3 = d + 1. For the constant c = 1.33114442478885300080049... see A253853. - _Vaclav Kotesovec_, Jan 18 2015
%t A253832 RecurrenceTable[{a[n]==a[n-1]*(1 + a[n-2]/a[n-4]), a[0]==1, a[1]==1, a[2]==1,a[3]==1},a,{n,0,20}] (* _Vaclav Kotesovec_, Jan 18 2015 *)
%t A253832 nxt[{a_,b_,c_,d_}]:={b,c,d,d(1+c/a)}; NestList[nxt,{1,1,1,1},20][[All,1]] (* _Harvey P. Dale_, Dec 27 2022 *)
%o A253832 (PARI) {a(n) = if( n<4, n>=0, a(n-1) * (1 + a(n-2) / a(n-4)))};
%o A253832 (Magma) I:=[1,1,1,1]; [n le 4 select I[n] else Self(n-1)*(1 + Self(n-2)/Self(n-4)): n in [1..20]]; // _G. C. Greubel_, Aug 03 2018
%Y A253832 Cf. A005831, A253853.
%K A253832 nonn
%O A253832 0,5
%A A253832 _Michael Somos_, Jan 17 2015