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

Author

Milan Janjic, Feb 14 2015

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

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}]

PARI

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

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