A143460 Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=9.

1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 43, 64, 94, 133, 181, 238, 304, 379, 463, 556, 685, 877, 1159, 1558, 2101, 2815, 3727, 4864, 6253, 7921, 9976, 12607, 16084, 20758, 27061, 35506, 46687, 61279, 80038, 103801, 133729, 171550, 219802, 282076

Offset: 0

Author

Alois P. Heinz, Aug 16 2008

Keywords

• nonn
• easy

Comments

a(n) is also the number of length n quaternary words with at least 9 0-digits between any other digits.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,3).

Crossrefs

9th column of A143461.

Programs

Maple

a := proc(k::nonnegint) local n,i,j; if k=0 then unapply (4^n,n) else unapply ((Matrix(k+1, (i,j)-> if (i=j-1) or j=1 and i=1 then 1 elif j=1 and i=k+1 then 3 else 0 fi)^(n+k))[1,1], n) fi end(9): seq (a(n), n=0..61);

Mathematica

Series[1/(1-x-3*x^10), {x, 0, 61}] // CoefficientList[#, x]& // Drop[#, 9]& (* Jean-François Alcover, Feb 13 2014 *)

Formula

G.f.: 1/(x^9*(1-x-3*x^10)).