

A255115


Number of nlength 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
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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*x1).  Colin Barker, Feb 15 2015
a(n) = A052912(n)+A052912(n2).  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*x1) + 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



