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A255116 Number of n-length words on {0,1,2,3} in which 0 appears only in runs of length 2. 5
1, 3, 10, 33, 108, 354, 1161, 3807, 12483, 40932, 134217, 440100, 1443096, 4731939, 15516117, 50877639, 166828734, 547034553, 1793736576, 5881695930, 19286191449, 63239784075, 207364440015, 679951894392, 2229575035401, 7310818426248, 23972310961920 (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, M. D. Weiner, n 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 (3,0,3).

FORMULA

a(n+3) = 3*a(n+2) + 3*a(n) with n>1, a(0) = 1, a(1) = 3, a(2) = 10.

G.f.: -(x^2+1) / (3*x^3+3*x-1). - Colin Barker, Feb 15 2015

a(n) = A089978(n) + A089978(n-2). - R. J. Mathar, Aug 04 2019

MATHEMATICA

RecurrenceTable[{a[0] == 1, a[1] == 3,  a[2]== 10, a[n] == 3 a[n - 1] + 3 a[n - 3]}, a[n], {n, 0, 25}]

PROG

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

CROSSREFS

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

Sequence in context: A060557 A018920 A271943 * A006190 A020704 A289450

Adjacent sequences:  A255113 A255114 A255115 * A255117 A255118 A255119

KEYWORD

nonn,easy

AUTHOR

Milan Janjic, Feb 14 2015

STATUS

approved

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Last modified September 20 17:04 EDT 2020. Contains 337265 sequences. (Running on oeis4.)