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A255119
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Number of n-length words on {0,1,2,3,4,5,6} in which 0 appears only in runs of length 2.
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1
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1, 6, 37, 228, 1404, 8646, 53244, 327888, 2019204, 12434688, 76575456, 471567960, 2904015888, 17883548064, 110130696144, 678208272192, 4176550921536, 25720089706080, 158389787869632, 975398032747008, 6006708734718528, 36990591135528960
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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) = 6*a(n+2) + 6*a(n) with n>1, a(0) = 1, a(1) = 6, a(2) = 37.
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MATHEMATICA
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RecurrenceTable[{a[0] == 1, a[1] == 6, a[2]== 37, a[n] == 6 a[n - 1] + 6 a[n - 3]}, a[n], {n, 0, 20}]
LinearRecurrence[{6, 0, 6}, {1, 6, 37}, 30] (* Harvey P. Dale, Nov 06 2017 *)
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PROG
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(PARI) Vec(-(x^2+1)/(6*x^3+6*x-1) + O(x^100)) \\ Colin Barker, Feb 15 2015
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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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