0,4

Toss a fair coin n times; a(n) is number of tosses having a run of 2 or more heads.

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

Row sums of triangle A153281 = (1, 3, 8, 19, 43,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 23 2008]

Feller, W.; An Introduction to Probability Theory and Its Application, Vol. 1, 2nd ed. New York: Wiley, p. 300, 1968.

T. D. Noe, Table of n, a(n) for n=0..300

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1020

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

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

G.f.: x^2/((1-2x)(1-x-x^2)) - Paul Barry (pbarry(AT)wit.ie), Feb 16 2004

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

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

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

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

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

Table[2^n-Fibonacci[n+2], {n, 0, 20}] (Vladimir Orlovsky, Jul 22 2008)

Cf. A050227.

a(n) = A101220(2, 2, n-1), for n > 0.

Cf. A050231, A050232, A050233

A153281 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 23 2008]

Adjacent sequences: A008463 A008464 A008465 this_sequence A008467 A008468 A008469

Sequence in context: A099050 A065352 A161993 this_sequence A102712 A054480 A121551

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com), Jack Kennedy (kennedy(AT)oldnews.org), Eric Weisstein (eric(AT)weisstein.com)