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.

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

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)/(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

Adjacent sequences: A152878 A152879 A152880 * A152882 A152883 A152884

Keyword

nonn,easy

Author

Emeric Deutsch, Jan 04 2009

Status

approved