A335690 a(1) = 1, a(2) = a(3) = 2; a(n) = (a(n-1) + a(n-2) + 1)/a(n-3) (for n>3).

1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4, 5, 2, 2, 1, 2, 2, 5, 4

Offset: 1

Author

N. J. A. Sloane, Jul 19 2020

Keywords

• nonn

Comments

This is another illustration of the 8-cycle discovered by H. Todd - see Lyness, Note 1847. Compare A076844. - N. J. A. Sloane, Jul 19 2020

Links

• R. C. Lyness, Note 1581. Cycles, Math. Gazette, 26 (1942), 62.
• R. C. Lyness, Note 1847. Cycles, Math. Gaz., 29 (1945), 231-233.
• R. C. Lyness, Note 2952. Cycles, Math. Gaz., 45 (1961), 207-209.

Crossrefs

Cf. A076839, A076844.

Programs

Maple

a := 1; b := 1; c := 1; f := proc(n) option remember; global a,b,c; if n=1 then RETURN(a); fi; if n=2 then RETURN(b); fi; if n=3 then RETURN(c); fi; RETURN((f(n-1)+f(n-2)+1)/f(n-3)); end;

Mathematica

RecurrenceTable[{a[1]==1,a[2]==a[3]==2,a[n]==(a[n-1]+a[n-2]+1)/a[n-3]},a,{n,90}] (* or *) PadRight[{},90,{1,2,2,5,4,5,2,2}] (* Harvey P. Dale, May 28 2021 *)