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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

(list; graph; refs; listen; history; text; internal format)

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}]