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A065094 a(1) = 1, a(n+1) is the sum of a(n) and floor( arithmetic mean of a(1) ... a(n) ). 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)