A253832 a(n) = a(n-1) * (1 + a(n-2)/a(n-4)), a(0) = a(1) = a(2) = a(3) = 1.
1, 1, 1, 1, 2, 4, 12, 60, 420, 6720, 241920, 27336960, 15773425920, 64182070068480, 4184799332605032960, 9825130460280752853949440, 2606675287692747620296839987164160, 399035505430293222012069797891526139192304640
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..27
Programs
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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
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Mathematica
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 *) 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 *) -
PARI
{a(n) = if( n<4, n>=0, a(n-1) * (1 + a(n-2) / a(n-4)))};
Formula
0 = a(n)*(a(n+3) - a(n+4)) + a(n+2)*a(n+3) for all n >= 0.
a(n+1) = a(n) * A253853(n) for all n >= 0.
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
Comments