A143459 Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=8.

1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 40, 61, 91, 130, 178, 235, 301, 376, 460, 580, 763, 1036, 1426, 1960, 2665, 3568, 4696, 6076, 7816, 10105, 13213, 17491, 23371, 31366, 42070, 56158, 74386, 97834, 128149, 167788, 220261, 290374, 384472, 510682

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 8 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 (1,0,0,0,0,0,0,0,3).

Crossrefs

8th 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(8): seq (a(n), n=0..58);

Mathematica

Series[1/(1-x-3*x^9), {x, 0, 58}] // CoefficientList[#, x]& // Drop[#, 8]& (* Jean-François Alcover, Feb 13 2014 *)

Formula

G.f.: 1/(x^8*(1-x-3*x^9)).