A255117 Number of n-length words on {0,1,2,3,4} in which 0 appears only in runs of length 2.

1, 4, 17, 72, 304, 1284, 5424, 22912, 96784, 408832, 1726976, 7295040, 30815488, 130169856, 549859584, 2322700288, 9811480576, 41445360640, 175072243712, 739534897152, 3123921031168, 13195973099520, 55742031986688, 235463812071424, 994639140683776

Offset

0,2

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 (4,0,4).

Formula

a(n+3) = 4*a(n+2) + 4*a(n) with n>1, a(0) = 1, a(1) = 4, a(2) = 17.

G.f.: -(x^2+1) / (4*x^3+4*x-1). - Colin Barker, Feb 15 2015

a(n) = A089979(n) + A089979(n-2). - R. J. Mathar, Aug 04 2019

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 4,  a[2]== 17, a[n] == 4 a[n - 1] + 4 a[n - 3]}, a[n], {n, 0, 25}]

Prog

(PARI) Vec(-(x^2+1)/(4*x^3+4*x-1) + O(x^100)) \\ Colin Barker, Feb 15 2015

Crossrefs

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

Sequence in context: A108929 A297578 A022031 * A001076 A122451 A257388

Adjacent sequences: A255114 A255115 A255116 * A255118 A255119 A255120

Keyword

nonn,easy

Author

Milan Janjic, Feb 14 2015

Status

approved