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A108758
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a(n)=2*a(n-1)-a(n-4)+a(n-5) with a(-2)=a(-1)=a(0)=1, a(1)=2, a(2)=4, a(3)=7.
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1, 1, 1, 2, 4, 7, 14, 27, 52, 101, 195, 377, 729, 1409, 2724, 5266, 10180, 19680, 38045, 73548, 142182, 274864, 531363, 1027223, 1985812, 3838942, 7421385, 14346910, 27735231, 53617332, 103652221, 200378917, 387369513, 748856925, 1447678961
(list; graph; refs; listen; history; internal format)
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OFFSET
| -2,4
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COMMENTS
| An unbiased coin is tossed n times and the resulting sequence of heads and tails is written linearly. Number of strings out of 2^n posiible strings, having no three consecutive heads (HHH's) is given by the above sequence (with suitable offset).
Starting (1, 1, 2, 4, 7,...) = INVERT transform of (1, 1, 0, 1, 1, 1, 1,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 27 2009]
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FORMULA
| G.f.: x*(1-x)/(1-2*x+x^4-x^5)+1 [Vladimir Kruchinin kru(AT)ie.tusur.ru, May 11 2011]
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MATHEMATICA
| a[n_] := a[n] = 2a[n - 1] - a[n - 4] + a[n - 5]; a[ -2] = a[ -1] = a[0] = 1; a[1] = 2; a[2] = 4; a[3] = 7; Table[ a[n], {n, 0, 32}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 25 2005)
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CROSSREFS
| Sequence in context: A123196 A079968 A001631 * A018085 A167751 A190822
Adjacent sequences: A108755 A108756 A108757 * A108759 A108760 A108761
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KEYWORD
| nonn,easy
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AUTHOR
| Mrs. J. P. Shiwalkar (jyotishiwalkar(AT)rediffmail.com) and M. N. Deshpande (dpratap_ngp(AT)sancharnet.in), Jun 24 2005
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 25 2005
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