OFFSET
1,2
LINKS
P. Chinn and S. Heubach, Integer Sequences Related to Compositions without 2's, J. Integer Seqs., Vol. 6 no. 2, 2003, Article 03.2.3.
J. J. Madden, A generating function for the distribution of runs in binary words, arXiv:1707.04351, Theorem 1.1, r=2, k=1.
FORMULA
a(n) = c(0)c(n-1) + c(1)c(n-2) + c(2)c(n-3) + ... + c(n-1)c(0), where c(i) is given by sequence A005251; generating function = (x(1-x)^2)/(1-2x+x^2-x^3)^2
a(n) = Sum_{k=1..floor((n+2)/3)} k*binomial(n-k+1, 2*k-1). - Vladeta Jovovic, Apr 10 2004
EXAMPLE
a(4)=6 since the compositions of 4 that do not contain a 2 are 1+1+1+1, 1+3, 3+1 and 4, for a total of 6 1's. Also there are 6 occurrences of 5 in the compositions of 8 (= 4+5-1): 1+1+1+5, 1+1+5+1, 1+5+1+1, 5+1+1+1, 5+3 and 3+5 (only compositions without 2's that contain a 5 are listed).
MATHEMATICA
Rest[CoefficientList[ Normal[Series[x(1 - x)^2/((1 - 2x + x^2 - x^3)^2), {x, 0, 50}]], x]]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Silvia Heubach (sheubac(AT)calstatela.edu), Jan 23 2003
STATUS
approved