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A109634
Number of 1's that appear among all ternary strings of length n that contain no consecutive 1's.
0
0, 1, 4, 16, 56, 188, 608, 1920, 5952, 18192, 54976, 164608, 489088, 1443776, 4238336, 12382208, 36022272, 104407296, 301618176, 868765696, 2495715328, 7152286720, 20452548608, 58369409024, 166276481024, 472876388352
OFFSET
0,3
REFERENCES
Ralph P. Grimaldi, Ternary Strings with No Consecutive 1's, Ars Combin. 89 (2008), 321-343.
FORMULA
(sqrt(3)/18)*((1+sqrt(3))^n - (1-sqrt(3))^n)+(n/12)*((1+sqrt(3))^(n+1)+(1-sqrt(3))^(n+1))
Conjecture: a(n)=A073388(n-1). [From R. J. Mathar, Aug 18 2008]
MATHEMATICA
f[n_] := Simplify[(2Sqrt[3] (-(1 - Sqrt[3])^n + (1 + Sqrt[3])^n) + 3n*((1 - Sqrt[3])^(1 + n) + (1 + Sqrt[3])^(1 + n)))/36]; Table[ f[n], {n, 0, 25}] (* Robert G. Wilson v *)
CROSSREFS
Sequence in context: A340257 A261386 A073388 * A026126 A026155 A025182
KEYWORD
nonn
AUTHOR
Ralph P. Grimaldi (ralph.grimaldi(AT)rose-hulman.edu), Aug 03 2005
EXTENSIONS
More terms from Robert G. Wilson v, Aug 05 2005
STATUS
approved