A151794 a(1)=2, a(2)=4, a(3)=6; a(n+3) = a(n+2)+ 2*a(n), n>=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

Offset: 1

Author

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

Keywords

• nonn
• easy

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).

Programs

Mathematica

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

PARI

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

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