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A255633
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Number of n-length words on {0,1,2,3,4,5} avoiding runs of zeros of length 1 (mod 3).
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5
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1, 5, 26, 136, 710, 3706, 19346, 100990, 527186, 2752006, 14365970, 74992966, 391476866, 2043580150, 10667858546, 55688153926, 290702250530, 1517518403926, 7921720943186, 41352818219110, 215869201519106, 1126876333254646, 5882498575587890, 30707708087054086
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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) = 5*a(n+2) + 6*a(n) with n > 0, a(0) = 1, a(1) = 5, a(2) = 26.
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MATHEMATICA
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RecurrenceTable[{a[0] == 1, a[1] == 5, a[2] == 26, a[n] == 5* a[n - 1] + 6*a[n - 3]}, a[n], {n, 0, 20}]
LinearRecurrence[{5, 0, 6}, {1, 5, 26}, 30] (* Harvey P. Dale, Aug 11 2023 *)
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PROG
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(PARI) Vec((1 + x^2)/(1 - 5*x - 6*x^3) + O(x^30)) \\ Andrew Howroyd, May 01 2020
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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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EXTENSIONS
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STATUS
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approved
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