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Search: id:A065094
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| A065094 |
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a(1) = 1, a(n+1) is the sum of a(n) and floor( arithmetic mean of a(1) ... a(n) ). |
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+0
8
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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?
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
Index entries for sequences related to Bessel functions or polynomials
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FORMULA
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a(1) = 1, a(n+1) = a(n) + floor((a(1) + a(2) + ... + a(n))/n)
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EXAMPLE
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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
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MAPLE
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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:
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MATHEMATICA
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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} ]
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PROGRAM
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(PARI) { for (n=1, 1000, if (n==1, s=0; a=1, s+=a; a+=s\(n - 1)); write("b065094.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 06 2009]
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CROSSREFS
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Cf. A065095.
Sequence in context: A116634 A035960 A023893 this_sequence A094023 A123630 A145728
Adjacent sequences: A065091 A065092 A065093 this_sequence A065095 A065096 A065097
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KEYWORD
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nonn,easy
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com)
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