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 A177795 Number of length n binary words that have at least one maximal run of 1's having length two. 0
 0, 1, 2, 5, 11, 25, 55, 120, 258, 550, 1163, 2444, 5108, 10627, 22021, 45474, 93621, 192232, 393779, 804947, 1642355, 3345307, 6803734, 13818636, 28031472, 56798821, 114971348, 232507076, 469801235, 948538807, 1913759614, 3858660525, 7775454390, 15659429797 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For bit strings of length 1,2,3,.. the sequence gives the number of strings of that length that contain at least one '11' not flanked by 1's; i.e., an occurrence of '0110' is OK; an occurrence of '0111' does not count. Thus the strings '0110011' and '0110111' are counted but '0111000' is not because '11' does not occur by itself. LINKS FORMULA a(n) = 2*a(n-1) + 2^n-3 - a(n-3) - 2^n-4 + a(n-4). a(n) = 2^n - A049856(n+3) = Sum_{k>=1} A218196(n+1,k). G.f.: (1 - x)^2*x^2/((1-2*x)*(1 - 2*x + x^3 -x^4)). - Geoffrey Critzer, Jan 23 2014 EXAMPLE a(5) = 11 because we have: 00011, 00110, 01011, 01100, 01101, 10011, 10110, 11000, 11001, 11010, 11011. - Geoffrey Critzer, Jan 23 2014 MATHEMATICA nn=30; r=Solve[{s==1+x s+x c+x a, a==x s, b==x a, c==x b+x c, d==x b+2x d}, {s, a, b, c, d}]; Drop[Flatten[CoefficientList[Series[b+d/.r, {x, 0, nn}], x]], 1] (* Geoffrey Critzer, Jan 23 2014 *) CROSSREFS Sequence in context: A291552 A208739 A291737 * A092685 A172481 A151529 Adjacent sequences:  A177792 A177793 A177794 * A177796 A177797 A177798 KEYWORD easy,nonn AUTHOR Oskars Rieksts (rieksts(AT)kutztown.edu), May 13 2010 EXTENSIONS Better name and more terms from Geoffrey Critzer, Jan 23 2014 STATUS approved

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Last modified June 22 12:30 EDT 2021. Contains 345379 sequences. (Running on oeis4.)