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A248959
Number of ternary words of length n in which all digits 0..2 occur in every subword of 4 consecutive digits.
2
1, 3, 9, 27, 36, 72, 132, 240, 444, 816, 1500, 2760, 5076, 9336, 17172, 31584, 58092, 106848, 196524, 361464, 664836, 1222824, 2249124, 4136784, 7608732, 13994640, 25740156, 47343528, 87078324, 160162008, 294583860, 541824192, 996570060, 1832978112
OFFSET
0,2
COMMENTS
For n < 4 the constraint is voidly satisfied: each of the n-digit words satisfies the definition since there is no subword of length 4. - M. F. Hasler, Jan 13 2015
LINKS
FORMULA
G.f.: (1 + 2*x + 5*x^2 + 14*x^3 - 3*x^4 - 3*x^6)/(1 - x - x^2 - x^3). - Corrected by Colin Barker, Jan 12 2015
a(n) = a(n-1) + a(n-2) + a(n-3).
a(n) = A001590(n+1) * 12, for n>=4.
a(n) = A196700(n) * 6, for n>=4. - Alois P. Heinz, Jan 12 2015
MATHEMATICA
Join[{1, 3, 9, 27}, LinearRecurrence[{1, 1, 1}, {36, 72, 132}, 30]] (* Harvey P. Dale, Mar 12 2015 *)
PROG
(PARI) Vec((1+2*x+5*x^2+14*x^3-3*x^4-3*x^6)/(1-x-x^2-x^3) + O(x^100)) \\ Colin Barker, Jan 12 2015; extended to indices 0..3 by M. F. Hasler, Jan 13 2015
CROSSREFS
Sequence in context: A305617 A292390 A211219 * A070362 A027889 A360423
KEYWORD
nonn,easy
AUTHOR
Andrew Woods, Jan 12 2015
EXTENSIONS
a(0)-a(3) from M. F. Hasler, Jan 13 2015
STATUS
approved