A100482 a(1) = 1 thereafter a(n) = Sum_{k=1..n-1} ceiling(a(n-k)/k).

1, 1, 2, 4, 7, 12, 21, 34, 55, 88, 143, 227, 361, 572, 908, 1439, 2279, 3607, 5709, 9033, 14294, 22615, 35779, 56605, 89551, 141671, 224123, 354561, 560908, 887349, 1403769, 2220732, 3513150, 5557727, 8792198, 13909056, 22003809, 34809516

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Maple

a[1]:=1: for n from 2 to 40 do a[n]:=sum(ceil(a[n-k]/k), k=1..n-1) od:seq(a[n], n=1..40);

Mathematica

a[n_]:= a[n]= If[n==1, 1, Sum[Ceiling[a[n-k]/k], {k, n-1}]];
Table[a[n], {n, 50}] (* G. C. Greubel, Apr 05 2023 *)

Prog

(SageMath)
@CachedFunction
def a(n): # a = A100482
    if (n==1): return 1
    else: return sum( ((a(n-k)+k-1)//k) for k in range(1, n) )
[a(n) for n in range(1, 51)] # G. C. Greubel, Apr 05 2023

Crossrefs

Cf. A100483.

Sequence in context: A168368 A305106 A182746 * A301762 A003293 A192759

Adjacent sequences: A100479 A100480 A100481 * A100483 A100484 A100485

Keyword

easy,nonn

Author

Leroy Quet, Nov 22 2004

Extensions

More terms from Emeric Deutsch, Dec 09 2004

Status

approved