OFFSET
0,3
COMMENTS
a(n)=Sum(k*A119914(n,k),k>=0).
Binomial transform of A179608. - Johannes W. Meijer, Aug 01 2010
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-3,-9).
FORMULA
G.f. = z(1-z)/[(1+z)(1-3z)^2].
a(n) = ((-1)^(n-1)+(3+4*n)*3^(n-1))/8. - Johannes W. Meijer, Aug 01 2010
EXAMPLE
a(2)=4 because in the nine ternary words of length 2, namely, 00, (0)1, (0)2, 1(0), 11, 12, 2(0), 21, 22, we have altogether 4 runs of 0's of odd length (shown between parentheses).
MAPLE
g:=z*(1-z)/(1-3*z)^2/(1+z): gser:=series(g, z=0, 35): seq(coeff(gser, z, n), n=0..28);
MATHEMATICA
LinearRecurrence[{5, -3, -9}, {0, 1, 4}, 30] (* Harvey P. Dale, Feb 18 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 29 2006
STATUS
approved