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A255630
Number of n-length ternary words avoiding runs of zeros of length 1 (mod 3).
4
1, 2, 5, 13, 32, 79, 197, 490, 1217, 3025, 7520, 18691, 46457, 115474, 287021, 713413, 1773248, 4407559, 10955357, 27230458, 67683593, 168233257, 418157888, 1039366555, 2583432881, 6421339426, 15960778517, 39671855677, 98607729632
OFFSET
0,2
FORMULA
a(n+3) = 2*a(n+2) + 3*a(n) with n > 0, a(0) = 1, a(2) = 2, a(3) = 5.
G.f.: ( -1-x^2 ) / ( -1+2*x+3*x^3 ). - R. J. Mathar, Aug 07 2015
a(n) = A099525(n)+A099525(n-2). - R. J. Mathar, Aug 07 2015
MATHEMATICA
RecurrenceTable[{a[0] == 1, a[2] == 2, a[3] == 5, a[n] == 2* a[n - 1] + 3*a[n - 3]}, a[n], {n, 0, 29}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Milan Janjic, Feb 28 2015
STATUS
approved