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

0,5

Comments

This sequence is similar to A005831 except for the division.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..27

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

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 *)

Prog

(PARI) {a(n) = if( n<4, n>=0, a(n-1) * (1 + a(n-2) / a(n-4)))};
(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

Crossrefs

Cf. A005831, A253853.

Sequence in context: A118456 A326861 A013202 * A004400 A005831 A136512

Adjacent sequences: A253829 A253830 A253831 * A253833 A253834 A253835

Keyword

nonn

Author

Michael Somos, Jan 17 2015

Status

approved