A320357 a(0)=1; a(1)=1; for n >= 2, a(n) = a(n-1) + a(n-A000005(n)).

1, 1, 2, 3, 4, 7, 9, 16, 20, 29, 38, 67, 76, 143, 181, 248, 315, 563, 639, 1202, 1383, 1946, 2585, 4531, 4846, 7431, 10016, 14547, 17132, 31679, 34264, 65943, 75959, 107638, 141902, 207845, 222392, 430237, 572139, 779984, 855943, 1635927, 1777829, 3413756, 3985895, 4765879

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..9000

Vaclav Kotesovec, Graph a(n+1)/a(n)

Formula

1 <= a(n+1)/a(n) <= 2. - Vaclav Kotesovec, Oct 14 2018

By empirical observation a(n) ~ 3.179662855437*exp(0.3175*n). - Ctibor O. Zizka, Oct 15 2018

Example

a(4) = a(3)+a(1) = a(2)+a(1)+a(1) = a(1)+a(0)+a(1)+a(1) = 4.

Mathematica

a[n_] := a[n] = If[n < 2, 1, a[n-1] + a[n - DivisorSigma[0, n]]]; Table[a[n], {n, 0, 50}] (* Vaclav Kotesovec, Oct 14 2018 *)

Crossrefs

Cf. A000005, A155043, A320520.

Sequence in context: A324736 A293853 A067236 * A250255 A070763 A295619

Adjacent sequences: A320354 A320355 A320356 * A320358 A320359 A320360

Keyword

nonn

Author

Ctibor O. Zizka, Oct 11 2018

Status

approved