A255118 Number of n-length words on {0,1,2,3,4,5} in which 0 appears only in runs of length 2.

1, 5, 26, 135, 700, 3630, 18825, 97625, 506275, 2625500, 13615625, 70609500, 366175000, 1898953125, 9847813125, 51069940625, 264844468750, 1373461409375, 7122656750000, 36937506093750, 191554837515625, 993387471328125, 5151624887109375, 26715898623125000

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 (5,0,5).

Formula

a(n+3) = 5*a(n+2) + 5*a(n) with n>1, a(0) = 1, a(1) = 5, a(2) = 26.

G.f.: -(x^2+1) / (5*x^3+5*x-1). - Colin Barker, Feb 15 2015

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 5,  a[2]== 26, a[n] == 5 a[n - 1] + 5 a[n - 3]}, a[n], {n, 0, 20}]

Prog

(PARI) Vec(-(x^2+1)/(5*x^3+5*x-1) + O(x^100)) \\ Colin Barker, Feb 15 2015

Crossrefs

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

Sequence in context: A047755 A047768 A022032 * A052918 A255633 A255815

Adjacent sequences: A255115 A255116 A255117 * A255119 A255120 A255121

Keyword

nonn,easy

Author

Milan Janjic, Feb 14 2015

Status

approved