A255115 Number of n-length words on {0,1,2} in which 0 appears only in runs of length 2.

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

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, 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 (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