OFFSET

1,2

COMMENTS

From Charles R Greathouse IV, Jul 16 2024: (Start)

This sequence is unbounded.

Probably a(n) is around sqrt(n). Can this be made precise and proven?

Is there some n > 3 such that a(n) > a(k) + 1 for all k < n? In other words, do the record values increase by 1? (End)

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

MATHEMATICA

a[1] = 1; a[2] = 2; a[3] = 4;

a[n_] := a[n] = Floor[(a[n - 1] + a[n - 2] + n)/(a[n - 3] + 1)];

Table[a[n], {n, 1, 100}]

PROG

(PARI) first(n)=if(n<4, return(powers(2, n-1))); my(v=List([1, 2, 4])); for(k=4, n, listput(v, (v[k-1]+v[k-2]+k)\(v[k-3]+1))); Vec(v) \\ Charles R Greathouse IV, Jul 16 2024

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 09 2024

STATUS

approved