A250309 a(n) = a(n-1)*(1 + a(n-1)/a(n-3)), with a(0) = a(1) = a(2) = 1.

1, 1, 1, 2, 6, 42, 924, 143220, 488523420, 258285263294520, 465795819523189050504840, 444125576385425970712647062585372630520, 763680920404535561780141108036287312478667174369871222219397040

Offset: 0

Author

Michael Somos, Jan 16 2015

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..17

Crossrefs

Cf. A007660, A258113.

Programs

Magma

I:=[1,1,1]; [n le 3 select I[n] else Self(n-1)*(1 + Self(n-1)/Self(n-3)): n in [1..15]]; // G. C. Greubel, Aug 03 2018

Mathematica

RecurrenceTable[{a[n]==a[n-1]*(1 + a[n-1]/a[n-3]), a[0]==1, a[1]==1, a[2]==1},a,{n,0,12}] (* Vaclav Kotesovec, Jan 18 2015 *)

PARI

{a(n) = if( n<3, n>=0, a(n-1)*(1 + a(n-1)/a(n-3)))};

Formula

0 = a(n)*(a(n+2) - a(n+3)) + a(n+2)*a(n+2) for all n>=0.

A007660(n+1) = a(n)/a(n-1).

a(n) ~ b * f^(d^n), where b = 0.270887790039424376..., f = c^(2+sqrt(5)) = 1.574173161904651669837597516422779594... and d = (1+sqrt(5))/2. For the constant c = A258113 = 1.11305797590293193285359770716758491... see A007660. - Vaclav Kotesovec, Jan 18 2015