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A255813
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Numbers of words on {0,1,2,3} having no isolated zeros.
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1
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1, 3, 10, 34, 115, 388, 1309, 4417, 14905, 50296, 169720, 572707, 1932556, 6521263, 22005505, 74255899, 250570870, 845532298, 2853184279, 9627852832, 32488455385, 109629815881, 369937455865, 1248325741972, 4212380047936
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n+3) = 4*a(n+2) - 3*a(n+1)+ 3*a(n) with n>=0, a(0) = 1, a(1) = 3, a(2) = 10.
G.f.: (-1 + x - x^2)/(-1 + 4*x - 3*x^2 + 3*x^3). - R. J. Mathar, Nov 07 2015
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MATHEMATICA
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RecurrenceTable[{a[0] == 1, a[1] == 3, a[2]== 10, a[n] == 4 a[n - 1] - 3 a[n - 2] + 3 a[n - 3]}, a[n], {n, 0, 25}]
LinearRecurrence[{4, -3, 3}, {1, 3, 10}, 100] (* G. C. Greubel, Jun 02 2016 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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