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A152881
Positions of those 1's that are followed by a 0, summed over all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword.
4
0, 1, 5, 15, 40, 95, 213, 455, 940, 1890, 3720, 7194, 13710, 25805, 48055, 88665, 162272, 294865, 532395, 955795, 1707110, 3034836, 5372400, 9473700, 16646700, 29155225, 50908793, 88644915, 153952120, 266726195, 461066385, 795320159
OFFSET
1,3
COMMENTS
a(n) = Sum(k*A119469(n+1,k),k>=0).
For n>1, a(n-1) is the n-th antidiagonal sum of A213777. [Clark Kimberling, Jun 21 2012]
LINKS
Milan Janjić, Hessenberg Matrices and Integer Sequences, J. Int. Seq. 13 (2010) # 10.7.8.
A. F. Y. Zhao, Pattern Popularity in Multiply Restricted Permutations, Journal of Integer Sequences, 17 (2014), #14.10.3.
FORMULA
G.f.: z^2*(1+2z)/(1-z-z^2)^3.
a(n) = A001628(n-1) + 2*A001628(n-2), n>1, a(0)=0, a(1)=1. [Vladimir Kruchinin, Apr 26 2011]
EXAMPLE
a(4)=15 because the Fibonacci binary words of length 4 are 1110, 1111, 1101, 1010, 1011, 0110, 0111, 0101 and the positions of those 1's that are followed by a 0 are 3, 2, 1, 3, 1, 3 and 2; their sum is 15.
MAPLE
G := z^2*(1+2*z)/(1-z-z^2)^3: Gser := series(G, z = 0, 38): seq(coeff(Gser, z, n), n = 1 .. 34);
CROSSREFS
Cf. A119469.
Sequence in context: A348885 A132985 A022570 * A000333 A291225 A054888
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jan 04 2009
STATUS
approved