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

Author

Emeric Deutsch, Jan 04 2009

Keywords

• nonn
• easy

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]

Examples

			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.
		

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.
• Index entries for linear recurrences with constant coefficients, signature (3,0,-5,0,3,1).

Crossrefs

Cf. A119469.

Programs

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);

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]