A022855 a(n) = [ a(n-1)/a(1) ] + [ a(n-1)/a(2) ] + ... + [ a(n-1)/a(n-1) ] for n >= 3, with initial terms 1,1.

1, 1, 2, 5, 13, 35, 97, 271, 761, 2143, 6042, 17043, 48081, 135656, 382752, 1079939, 3047074, 8597406, 24257838, 68444231, 193117503, 544886995, 1537415492, 4337865331, 12239421132, 34533905116, 97438480950, 274925686472, 775711324186, 2188693483680, 6175466331563

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A022858, A022874.

Programs

Mathematica

Clear[a]; a[n_] := a[n] = If[n == 1, 1, Sum[Floor[a[n-1]/a[k]], {k, 1, n-1}]]; Table[a[n], {n, 1, 30}] (* Vaclav Kotesovec, May 22 2019 *)

Formula

a(n) ~ c * d^n, where d = 2.821530916787913161647514028120517886471375614018590071788760268658400644805..., c = 0.06693303886818014323088828992453194331872567432210373455545066012434187... - Vaclav Kotesovec, May 22 2019

Extensions

Name clarified by Robert C. Lyons, Feb 11 2025