(Translated by https://www.hiragana.jp/)
A255118 - OEIS
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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.
5
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
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
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
KEYWORD
nonn,easy
AUTHOR
Milan Janjic, Feb 14 2015
STATUS
approved