A143457 Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=6.

1, 4, 7, 10, 13, 16, 19, 22, 34, 55, 85, 124, 172, 229, 295, 397, 562, 817, 1189, 1705, 2392, 3277, 4468, 6154, 8605, 12172, 17287, 24463, 34294, 47698, 66160, 91975, 128491, 180352, 253741, 356623, 499717, 698197, 974122, 1359595, 1900651

Offset

0,2

Comments

a(n) is also the number of length n quaternary words with at least 6 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 (1,0,0,0,0,0,3).

Formula

G.f.: 1/(x^6*(1-x-3*x^7)).

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(6): seq (a(n), n=0..55);

Mathematica

Series[1/(1-x-3*x^7), {x, 0, 55}] // CoefficientList[#, x]& // Drop[#, 6]& (* Jean-François Alcover, Feb 13 2014 *)

Crossrefs

6th column of A143461.

Sequence in context: A004084 A121381 A310680 * A046956 A327139 A198265

Adjacent sequences: A143454 A143455 A143456 * A143458 A143459 A143460

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 16 2008

Status

approved