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.

Showing 1-3 of 3 results.

A208225 a(n)=(a(n-1)^3*a(n-3)^3+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

Original entry on oeis.org

1, 1, 1, 1, 2, 9, 731, 3124943137, 11123050014071530610530827873034
Offset: 0

Views

Author

Matthew C. Russell, Apr 25 2012

Keywords

Comments

This is the case a=3, 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).

Crossrefs

Programs

  • Maple
    y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^3*y(n-3)^3+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]^3+ a[n-2])/ a[n-4]},a,{n,10}] (* Harvey P. Dale, Aug 25 2016 *)

A208221 a(n)=(a(n-1)^2*a(n-3)^2+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

Original entry on oeis.org

1, 1, 1, 1, 2, 5, 27, 2921, 106653026, 1658455747832683945, 869174798276372512100586962107665002957113
Offset: 0

Views

Author

Matthew C. Russell, Apr 25 2012

Keywords

Comments

This is the case a=2, 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 97 digits. - Harvey P. Dale, Dec 17 2017

Crossrefs

Programs

  • Maple
    y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^2*y(n-3)^2+y(n-2))/y(n-4): end:
    seq(y(n),n=0..11);
  • Mathematica
    a[n_] := a[n] = If[n <= 3, 1, (a[n-1]^2*a[n-3]^2 + a[n-2])/a[n-4]];
    Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Nov 24 2017 *)
    RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]^2 a[n-3]^2+ a[n-2])/ a[n-4]},a,{n,12}] (* Harvey P. Dale, Dec 17 2017 *)

A208219 a(n)=(a(n-1)^3*a(n-3)+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

Original entry on oeis.org

1, 1, 1, 1, 2, 9, 731, 781235791, 2145650135491172007486084385, 802327342392981520933850619811649523436811893002103478524225246677189521545661182074
Offset: 0

Views

Author

Matthew C. Russell, Apr 25 2012

Keywords

Comments

This is the case a=1, 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).
The next term (a(10)) has 258 digits. - Harvey P. Dale, Sep 21 2016

Crossrefs

Programs

  • Maple
    y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^3*y(n-3)+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]+ a[n-2])/ a[n-4]},a,{n,10}] (* Harvey P. Dale, Sep 21 2016 *)
Showing 1-3 of 3 results.