login
A255117
Number of n-length words on {0,1,2,3,4} in which 0 appears only in runs of length 2.
5
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
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) = 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
KEYWORD
nonn,easy
AUTHOR
Milan Janjic, Feb 14 2015
STATUS
approved