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A065095 a(1) = 1, a(n+1) is the sum of a(n) and ceiling( arithmetic mean of a(1) ... a(n) ). 8
1, 2, 4, 7, 11, 16, 23, 33, 46, 62, 83, 110, 144, 186, 238, 303, 383, 481, 600, 744, 918, 1128, 1380, 1681, 2039, 2464, 2968, 3563, 4264, 5088, 6054, 7184, 8503, 10040, 11827, 13901, 16304, 19082, 22289, 25986, 30240, 35128, 40736, 47161, 54512 (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 = 0.78... and BesselI(b,x) is the modified Bessel function of the first kind. Can someone prove this?

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) + ceiling((a(1) + a(2) + ... + a(n))/n).

EXAMPLE

a(5) = a(4) + ceiling((a(1)+a(2)+a(3)+a(4))/4) = 7 + ceiling((1+2+4+7)/4) = 7 + floor(14/4) = 7 + 4 = 11.

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] + ceil(summe/j): flip := 1-flip: od:

MATHEMATICA

a[1] = 1; a[n_] := a[n] = a[n - 1] + Ceiling[ Sum[ a[i], {i, 1, n - 1} ]/(n - 1) ]; Table[ a[ n], {n, 1, 45} ]

PROG

(PARI) { for (n=1, 1000, if (n==1, s=0; a=1, s+=a; a+=ceil(s/(n - 1))); write("b065095.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 06 2009

CROSSREFS

Cf. A065094.

Sequence in context: A000601 A062433 A317910 * A005253 A212364 A320591

Adjacent sequences:  A065092 A065093 A065094 * A065096 A065097 A065098

KEYWORD

nonn,easy

AUTHOR

Ulrich Schimke (ulrschimke(AT)aol.com)

STATUS

approved

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Last modified September 20 05:51 EDT 2019. Contains 327212 sequences. (Running on oeis4.)