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Search: id:A065095
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| A065095 |
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a(1) = 1, a(n+1) is the sum of a(n) and ceiling( arithmetic mean of a(1) ... a(n) ). |
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8
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| 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; 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 = 0.78... 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) + ceil((a(1) + a(2) + ... + a(n))/n)
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EXAMPLE
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a(5) = a(4) + ceil((a(1)+a(2)+a(3)+a(4))/4) = 7 + ceil((1+2+4+7)/4) = 7 + floor(14/4) = 7 + 4 = 11
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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] + ceil(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] + Ceiling[ Sum[ a[i], {i, 1, n - 1} ]/(n - 1) ]; Table[ a[ n], {n, 1, 45} ]
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PROGRAM
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(PARI) { for (n=1, 1000, if (n==1, s=0; a=1, s+=a; a+=ceil(s/(n - 1))); write("b065095.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 06 2009]
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CROSSREFS
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Cf. A065094.
Sequence in context: A114805 A000601 A062433 this_sequence A005253 A129339 A011912
Adjacent sequences: A065092 A065093 A065094 this_sequence A065096 A065097 A065098
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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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