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 n-1 to n+1. The results of the tosses are written in a linear array. Then the probability of non-occurrence 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.115-119.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,2).
FORMULA
G.f.: 2*x*(-x+x^2-1)/((1+x)*(2*x-1)).
a(n) = A084214(n), n>1.
a(n) = A168648(n-2), n>2.
a(n) = 2*A048573(n-2), n>1.
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^2-1)/((1+x)*(2*x-1)) + 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