A022021 Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(5,20).

5, 20, 81, 329, 1337, 5434, 22086, 89767, 364852, 1482917, 6027219, 24497237, 99567416, 404685244, 1644816681, 6685249720, 27171759829, 110437838993, 448867366641, 1824392026070, 7415121953942, 30138277741915, 122495056843392, 497873139253657, 2023572780632275

Offset: 0

Author

R. K. Guy

Keywords

• nonn

Comments

This coincides with the linearly recurrent sequence defined by the expansion of (5 - 4*x^2)/(1 - 4*x - x^2 + 3*x^3) only up to n <= 39. - Bruno Berselli, Feb 11 2016

Links

• Colin Barker, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A022018 - A022025, A022026 - A022032.

Programs

Maple

A022021 := proc(n)
    option remember;
    if n <= 1 then
        op(n+1,[5,20]) ;
    else
        a := procname(n-1)^2/procname(n-2) ;
        if type(a,'integer') then
            a+1 ;
        else
            ceil(a) ;
        fi;
    end if;
end proc: # R. J. Mathar, Feb 10 2016

PARI

a=[5,20];for(n=2,30,a=concat(a,a[n]^2\a[n-1]+1));a \\ M. F. Hasler, Feb 10 2016

Formula

a(n+1) = floor(a(n)^2/a(n-1))+1 for all n > 0. - M. F. Hasler, Feb 10 2016

Extensions

Double-checked and extended to 3 lines of data by M. F. Hasler, Feb 10 2016