A208225 -id:A208225

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A208222

a(n) = (a(n-1)^3*a(n-3)^2+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

+10
4

1, 1, 1, 1, 2, 9, 731, 1562471573, 154486807085783774292345385804

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

This is the case a=2, b=1, c=3, y(0)=y(1)=y(2)=y(3)=1 of the recurrence shown in the Example 3.3 of "The Laurent phenomenon" (see Link lines, p. 10).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..11

Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001), Advances in Applied Mathematics 28 (2002), 119-144.

MAPLE

y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^3*y(n-3)^2+y(n-2))/y(n-4): end:

seq(y(n), n=0..9);

MATHEMATICA

a[n_]:=If[n<4, 1, (a[n - 1]^3*a[n - 3]^2 + a[n - 2])/a[n - 4]]; Table[a[n], {n, 0, 11}] (* Indranil Ghosh, Mar 19 2017 *)

nxt[{a_, b_, c_, d_}]:={b, c, d, (d^3 b^2+c)/a}; NestList[nxt, {1, 1, 1, 1}, 10][[All, 1]] (* Harvey P. Dale, May 31 2020 *)

CROSSREFS

Cf. A048736, A208219, A208221, A208225.

KEYWORD

nonn

AUTHOR

Matthew C. Russell, Apr 25 2012

STATUS

approved

A208224

a(n)=(a(n-1)^2*a(n-3)^3+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

+10
4

1, 1, 1, 1, 2, 5, 27, 5837, 2129410576, 17850077316687753782569, 2346851008195218976646246398770505953580095510848345967

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

This is the case a=3, b=1, c=2, y(0)=y(1)=y(2)=y(3)=1 of the recurrence shown in the Example 3.3 of "The Laurent phenomenon" (see Link lines, p. 10).

The next term (a(11)) has 133 digits. - Harvey P. Dale, Mar 06 2017

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..13

Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001), Advances in Applied Mathematics 28 (2002), 119-144.

MAPLE

y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^2*y(n-3)^3+y(n-2))/y(n-4): end:

seq(y(n), n=0..11);

MATHEMATICA

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1, a[n]==(a[n-1]^2*a[n-3]^3+ a[n-2])/ a[n-4]}, a, {n, 10}] (* Harvey P. Dale, Mar 06 2017 *)

CROSSREFS

Cf. A048736, A208221, A208223, A208225, A208227.

KEYWORD

nonn

AUTHOR

Matthew C. Russell, Apr 25 2012

STATUS

approved

A208228

a(n)=(a(n-1)^3*a(n-3)^4+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

+10
3

1, 1, 1, 1, 2, 9, 731, 6249886265, 800859597553373777918076329400178

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

This is the case a=4, b=1, c=3, y(0)=y(1)=y(2)=y(3)=1 of the recurrence shown in the Example 3.3 of "The Laurent phenomenon" (see Link lines, p. 10).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10

Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001), Advances in Applied Mathematics 28 (2002), 119-144.

MAPLE

y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^3*y(n-3)^4+y(n-2))/y(n-4): end:

seq(y(n), n=0..9);

MATHEMATICA

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1, a[n]==(a[n-1]^3 a[n-3]^4+ a[n-2])/ a[n-4]}, a, {n, 10}] (* Harvey P. Dale, Jan 08 2014 *)

CROSSREFS

Cf. A048736, A208225, A208227.

KEYWORD

nonn

AUTHOR

Matthew C. Russell, Apr 25 2012

STATUS

approved

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