A119916 Number of runs of 0's of odd length in all ternary words of length n.

0, 1, 4, 17, 64, 233, 820, 2825, 9568, 31985, 105796, 346913, 1129312, 3653657, 11758132, 37665881, 120172096, 382039649, 1210689028, 3825777329, 12058462720, 37918780361, 118986517684, 372650082857, 1165021837984

Offset: 0

Author

Emeric Deutsch, May 29 2006

Keywords

• nonn
• easy

Comments

a(n)=Sum(k*A119914(n,k),k>=0).

Binomial transform of A179608. - Johannes W. Meijer, Aug 01 2010

Examples

			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).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-3,-9).

Crossrefs

Cf. A119914.

Programs

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 *)

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