A143456 Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=5.

1, 4, 7, 10, 13, 16, 19, 31, 52, 82, 121, 169, 226, 319, 475, 721, 1084, 1591, 2269, 3226, 4651, 6814, 10066, 14839, 21646, 31324, 45277, 65719, 95917, 140434, 205372, 299344, 435175, 632332, 920083, 1341385, 1957501, 2855533, 4161058, 6058054

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 5 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 (1,0,0,0,0,3).

Crossrefs

5th 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(5): seq(a(n), n=0..52);

Mathematica

Series[1/(1-x-3*x^6), {x, 0, 52}] // CoefficientList[#, x]& // Drop[#, 5]& (* Jean-François Alcover, Feb 13 2014 *)

Formula

G.f.: 1/(x^5*(1-x-3*x^6)).