%I A008466
%S A008466 0,0,1,3,8,19,43,94,201,423,880,1815,3719,7582,15397,31171,62952,
%T A008466 126891,255379,513342,1030865,2068495,4147936,8313583,16655823,
%U A008466 33358014,66791053,133703499,267603416,535524643,1071563515
%N A008466 a(n) = 2^n-Fibonacci(n+2).
%C A008466 Toss a fair coin n times; a(n) is number of tosses having a run of 2 
               or more heads.
%C A008466 Also the number of binary words of length n with at least two neighboring 
               1 digits. For example, a(4)=8 because 8 binary words of length 4 
               have two or more neighboring 1 digits: 0011, 0110, 0111, 1011, 1100, 
               1101, 1110, 1111. - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 
               18 2008
%C A008466 Row sums of triangle A153281 = (1, 3, 8, 19, 43,...). [From Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Dec 23 2008]
%D A008466 Feller, W.; An Introduction to Probability Theory and Its Application, 
               Vol. 1, 2nd ed. New York: Wiley, p. 300, 1968.
%H A008466 T. D. Noe, <a href="b008466.txt">Table of n, a(n) for n=0..300</a>
%H A008466 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=1020">
               Encyclopedia of Combinatorial Structures 1020</a>
%H A008466 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Run.html">Link to a section of The World of Mathematics.</a>
%F A008466 a(1)=0, a(2)=1, a(3)=3, a(n)=3*a(n-1)-a(n-2)-2*a(n-3). E.g. a(8)=201=3*a(7)-a(6)-2*a(5)=3*94-43-2*19. 
               - Miklos Kristof (kristmikl(AT)freemail.hu), Nov 24 2003
%F A008466 G.f.: x^2/((1-2x)(1-x-x^2)) - Paul Barry (pbarry(AT)wit.ie), Feb 16 2004
%F A008466 Convolution of Fibonacci(n) and (2^n-0^n)/2. a(n)=sum{k=0..n, (2^k-0^k)Fib(n-k)/
               2}; a(n+1)=sum{k=0..n, Fib(k)2^(n-k)}=2^n*sum{k=0..n, Fib(k)/2^k}. 
               - Paul Barry (pbarry(AT)wit.ie), May 19 2004
%F A008466 a(n)=a(n-1)+a(n-2)+2^(n-2) E.g. a(7)=a(6)+a(5)+2^5=43+19+32=94 - Jon 
               Stadler (jstadler(AT)capital.edu), Aug 21 2006
%F A008466 a(n)= 2*a(n-1) + Fib(n-1) E.g. a(7) = 2*a(6) + Fib(6) = 2*43 + 8 = 94 
               - Thomas M. Green (tgreen(AT)astound.net), Aug 21 2007
%F A008466 a(n) = term (1,3) in the 3x3 matrix [3,1,0; -1,0,1; -2,0,0]^n. - Alois 
               P. Heinz (heinz(AT)hs-heilbronn.de), Jul 18 2008
%p A008466 a := n -> (Matrix([[3, 1, 0], [ -1, 0, 1], [ -2, 0, 0]])^(n))[1, 3]; 
               seq ((a(n)), n=0..50); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Jul 18 2008
%t A008466 Table[2^n-Fibonacci[n+2],{n,0,20}] (Vladimir Orlovsky, Jul 22 2008)
%Y A008466 Cf. A050227.
%Y A008466 a(n) = A101220(2, 2, n-1), for n > 0.
%Y A008466 Cf. A050231, A050232, A050233
%Y A008466 A153281 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 23 2008]
%Y A008466 Sequence in context: A099050 A065352 A161993 this_sequence A102712 A054480 
               A121551
%Y A008466 Adjacent sequences: A008463 A008464 A008465 this_sequence A008467 A008468 
               A008469
%K A008466 nonn,nice,easy
%O A008466 0,4
%A A008466 N. J. A. Sloane (njas(AT)research.att.com), Jack Kennedy (kennedy(AT)oldnews.org), 
               Eric Weisstein (eric(AT)weisstein.com)