A065094 a(1) = 1, a(n+1) is the sum of a(n) and floor( arithmetic mean of a(1) ... a(n) ).

1, 2, 3, 5, 7, 10, 14, 20, 27, 36, 48, 63, 82, 106, 136, 173, 218, 273, 341, 423, 522, 641, 784, 955, 1158, 1399, 1685, 2023, 2421, 2889, 3437, 4079, 4828, 5701, 6716, 7893, 9257, 10834, 12655, 14754, 17169, 19944, 23128, 26775, 30948, 35716, 41157

Offset

1,2

Comments

It seems that a(n) is asymptotic to C*BesselI(0,2*sqrt(n)) where C is a constant C = 0.44... and BesselI(b,x) is the modified Bessel function of the first kind. Can someone prove this?

A241772(n) = a(n+1) - a(n) = (Sum_{1..n} a(k)) / n. - Reinhard Zumkeller, Apr 28 2014

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for sequences related to Bessel functions or polynomials

Formula

a(1) = 1, a(n+1) = a(n) + floor((a(1) + a(2) + ... + a(n))/n).

Example

a(5) = a(4) + floor((a(1)+a(2)+a(3)+a(4))/4) = 5 + floor((1+2+3+5)/4) = 5 + floor(11/4) = 5 + 2 = 7.

Maple

a[1] := 1: summe := 0: flip := 1: for j from 1 to 100 do: print (j, a[flip]); summe := summe + a[flip]: a[1-flip] := a[flip] + floor(summe/j): flip := 1-flip: od:

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] + Floor[ Sum[ a[i], {i, 1, n - 1} ]/(n - 1) ]; Table[ a[n], {n, 1, 47} ]

Prog

(PARI) { for (n=1, 1000, if (n==1, s=0; a=1, s+=a; a+=s\(n - 1)); write("b065094.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 06 2009
(Haskell)
a065094 n = a065094_list !! (n-1)
a065094_list = 1 : f 1 1 1 where
   f k s x = y : f (k + 1) (s + y) y where y = x + div s k
-- Reinhard Zumkeller, Apr 28 2014

Crossrefs

Cf. A065095.

Sequence in context: A035960 A288254 A023893 * A145728 A145786 A094023

Adjacent sequences: A065091 A065092 A065093 * A065095 A065096 A065097

Keyword

nonn,easy

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Status

approved