A255119 Number of n-length words on {0,1,2,3,4,5,6} in which 0 appears only in runs of length 2.
1, 6, 37, 228, 1404, 8646, 53244, 327888, 2019204, 12434688, 76575456, 471567960, 2904015888, 17883548064, 110130696144, 678208272192, 4176550921536, 25720089706080, 158389787869632, 975398032747008, 6006708734718528, 36990591135528960
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3. example 10.
- Index entries for linear recurrences with constant coefficients, signature (6,0,6).
Programs
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Mathematica
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 *) -
PARI
Vec(-(x^2+1)/(6*x^3+6*x-1) + O(x^100)) \\ Colin Barker, Feb 15 2015
Formula
a(n+3) = 6*a(n+2) + 6*a(n) with n>1, a(0) = 1, a(1) = 6, a(2) = 37.
G.f.: -(x^2+1) / (6*x^3+6*x-1). - Colin Barker, Feb 15 2015