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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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).

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

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 *)

PROG

(PARI) Vec(-(x^2+1)/(6*x^3+6*x-1) + O(x^100)) \\ Colin Barker, Feb 15 2015

CROSSREFS

Cf. A000930, A239333, A239340, A254657, A254600, A254664.

Sequence in context: A288786 A180032 A022035 * A005668 A018904 A192807

Adjacent sequences: A255116 A255117 A255118 * A255120 A255121 A255122

KEYWORD

nonn,easy

AUTHOR

Milan Janjic, Feb 14 2015

STATUS

approved

URL: https://oeis.org/A255119

⇱ A255119 - OEIS