

A151794


a(1)=2, a(2)=4, a(3)=6; a(n+3) = a(n+2)+ 2*a(n), n>=1.


1



2, 4, 6, 14, 26, 54, 106, 214, 426, 854, 1706, 3414, 6826, 13654, 27306, 54614, 109226, 218454, 436906, 873814, 1747626, 3495254, 6990506, 13981014, 27962026, 55924054, 111848106, 223696214, 447392426, 894784854, 1789569706, 3579139414, 7158278826, 14316557654
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OFFSET

1,1


COMMENTS

Consider the following coin tossing experiment. Let n >= 1 be a predetermined integer. We toss an unbiased coin sequentially. For each outcome, we score two points for a head (H) and one point for a tail (T). The coin is tossed until the total score reaches n or jumps from n1 to n+1. The results of the tosses are written in a linear array. Then the probability of nonoccurrence of double heads (HH) is given by p(n) = a(n) / 2^n, n>=1.


REFERENCES

Bhanu K. S, Deshpande M. N. & Cholkar C. P. (2006): Coin tossing Some Surprising Results, International Journal of Mathematical Education In Science and Technology, Vol.37, No.1, pp.115119.


LINKS



FORMULA

G.f.: 2*x*(x+x^21)/((1+x)*(2*x1)).
a(n) = (4*(1)^n+5*2^n)/6 for n>1.  Colin Barker, Jun 12 2015


MATHEMATICA

Join[{2}, LinearRecurrence[{1, 2}, {4, 6}, 40]] (* Harvey P. Dale, Oct 19 2012 *)


PROG

(PARI) Vec(2*x*(x+x^21)/((1+x)*(2*x1)) + O(x^100)) \\ Colin Barker, Jun 12 2015


CROSSREFS



KEYWORD

nonn,easy


AUTHOR

K. S. Bhanu (bhanu_105(AT)yahoo.com), Jun 21 2009


STATUS

approved



