

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
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OFFSET

1,3


COMMENTS

a(n) = Sum(k*A119469(n+1,k),k>=0).
For n>1, a(n1) is the nth antidiagonal sum of A213777. [Clark Kimberling, Jun 21 2012]


LINKS

Table of n, a(n) for n=1..32.
M. Janjic, 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.
Index entries for linear recurrences with constant coefficients, signature (3,0,5,0,3,1).


FORMULA

G.f.: z^2*(1+2z)/(1zz^2)^3.
a(n) = A001628(n1) + 2*A001628(n2), 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)/(1zz^2)^3: Gser := series(G, z = 0, 38): seq(coeff(Gser, z, n), n = 1 .. 34);


CROSSREFS

Cf. A119469.
Sequence in context: A034182 A132985 A022570 * A000333 A291225 A054888
Adjacent sequences: A152878 A152879 A152880 * A152882 A152883 A152884


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, Jan 04 2009


STATUS

approved



