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A255115 Number of n-length words on {0,1,2} in which 0 appears only in runs of length 2. 5
1, 2, 5, 12, 28, 66, 156, 368, 868, 2048, 4832, 11400, 26896, 63456, 149712, 353216, 833344, 1966112, 4638656, 10944000, 25820224, 60917760, 143723520, 339087488, 800010496, 1887468032, 4453111040, 10506243072, 24787422208, 58481066496, 137974619136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Apparently a(n) =A239333(n).

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 (2,0,2).

FORMULA

a(n+3) = 2*a(n+2) + 2*a(n) with n>1, a(0) = 1, a(1) = 2, a(2)=5.

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

a(n) = A052912(n)+A052912(n-2). - R. J. Mathar, Jun 18 2015

MATHEMATICA

RecurrenceTable[{a[0] == 1, a[1] == 2,  a[2]== 5, a[n] == 2 a[n - 1] + 2 a[n - 3]}, a[n], {n, 0, 29}]

PROG

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

CROSSREFS

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

Sequence in context: A297496 A302020 A239333 * A166297 A024960 A291234

Adjacent sequences:  A255112 A255113 A255114 * A255116 A255117 A255118

KEYWORD

nonn,easy

AUTHOR

Milan Janjic, Feb 14 2015

STATUS

approved

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Last modified December 5 08:22 EST 2020. Contains 338944 sequences. (Running on oeis4.)