A249019 Number of ternary words of length n in which all digits 0..2 occur in every 6 consecutive digits.

1, 3, 9, 27, 81, 243, 540, 1440, 3804, 9960, 25908, 67344, 175884, 458832, 1196364, 3119304, 8134164, 21212832, 55316892, 144249168, 376159644, 980918904, 2557958964, 6670420704, 17394543180, 45359994336, 118285895244, 308455762488, 804364332180, 2097551985168, 5469815336796, 14263713072192

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,3,5,6,-1,-1,0,-1,-1).

Formula

a(n) = a(n-1) + 2*a(n-2) + 3*a(n-3) + 5*a(n-4) + 6*a(n-5) - a(n-6) - a(n-7) - a(n-9) - a(n-10), for n>=16.

G.f.: (1 + 2*x + 4*x^2 + 9*x^3 + 22*x^4 + 60*x^5 - 8*x^6 - 14*x^7 - 8*x^9 - 26*x^10 + 3*x^12 + 3*x^15)/(1 - x - 2*x^2 - 3*x^3 - 5* x^4 - 6*x^5 + x^6 + x^7 + x^9 + x^10 - Colin Barker, Jan 12 2015

Mathematica

LinearRecurrence[{1, 2, 3, 5, 6, -1, -1, 0, -1, -1}, {1, 3, 9, 27, 81, 243, 540, 1440, 3804, 9960, 25908, 67344, 175884, 458832, 1196364, 3119304}, 40] (* Harvey P. Dale, Feb 05 2019 *)

Prog

(PARI) Vec(-12*x^6*(20*x^9 +27*x^8 +9*x^7 +23*x^6 +28*x^5 -110*x^4 -138*x^3 -107*x^2 -75*x -45) / (x^10 +x^9 +x^7 +x^6 -6*x^5 -5*x^4 -3*x^3 -2*x^2 -x +1) + O(x^100)) \\ Colin Barker, Jan 12 2015

Crossrefs

Cf. A248959, A248960.

Sequence in context: A291007 A038002 A272338 * A216096 A300148 A190128

Adjacent sequences: A249016 A249017 A249018 * A249020 A249021 A249022

Keyword

nonn,easy

Author

Andrew Woods, Jan 12 2015

Status

approved