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