A248960 Number of ternary words of length n in which all digits 0..2 occur in every 5 consecutive digits.

1, 3, 9, 27, 81, 150, 366, 870, 2022, 4686, 10974, 25614, 59742, 139398, 325350, 759198, 1771590, 4134126, 9647262, 22512342, 52533750, 122590422, 286071414, 667563054, 1557794622, 3635198310, 8482932318, 19795382454, 46193598486, 107795266974, 251546100558, 586996465758, 1369788083022

Offset

0,2

Links

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

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

Formula

G.f.: (1+2*x+4*x^2+10*x^3+28*x^4-8*x^5-14*x^6-6*x^8+3*x^10) / ((1+x)*(1-2*x-2*x^3+x^5)). - Colin Barker, Oct 27 2016

a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-5) - a(n-6).

a(n) = A242317(n-4) * 6.

Mathematica

Join[{1, 3, 9, 27, 81}, LinearRecurrence[{1, 2, 2, 2, -1, -1}, {150, 366, 870, 2022, 4686, 10974}, 30]] (* Harvey P. Dale, Apr 04 2015 *)

Prog

(PARI) Vec((1+2*x+4*x^2+10*x^3+28*x^4-8*x^5-14*x^6-6*x^8+3*x^10)/((1+x)*(1-2*x-2*x^3+x^5)) + O(x^30)) \\ Colin Barker, Oct 27 2016

Crossrefs

Cf. A242317, A249019.

Sequence in context: A014950 A271351 A036143 * A006521 A289257 A014953

Adjacent sequences: A248957 A248958 A248959 * A248961 A248962 A248963

Keyword

nonn,easy

Author

Andrew Woods, Jan 12 2015

Extensions

Changed offset to 0. - N. J. A. Sloane, Jan 15 2015

Status

approved