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A287833 Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 2. 0
1, 11, 103, 967, 9079, 85243, 800351, 7514541, 70554457, 662439857, 6219685951, 58396989455, 548292695881, 5147951686649, 48334414751849, 453814602701801, 4260891430727991, 40005754941255473, 375616336261903907, 3526683405274793053, 33112233522155404139 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = 10*a(n-1) - 2*a(n-2) - 37*a(n-3) + 16*a(n-4) + 19*a(n-5) + a(n-6), a(0)=1, a(1)=11, a(2)=103, a(3)=967, a(4)=9079, a(5)=85243.
G.f.: (-1 - x + 5*x^2 + 4*x^3 - 6*x^4 - 3*x^5)/(-1 + 10*x - 2*x^2 - 37*x^3 + 16*x^4 + 19*x^5 + x^6).
MATHEMATICA
LinearRecurrence[{10, -2, -37, 16, 19, 1}, {1, 11, 103, 967, 9079, 85243}, 20]
PROG
(Python)
def a(n):
.if n in [0, 1, 2, 3, 4, 5]:
..return [1, 11, 103, 967, 9079, 85243][n]
.return 10*a(n-1) - 2*a(n-2) - 37*a(n-3) + 16*a(n-4) + 19*a(n-5) + a(n-6)
CROSSREFS
Sequence in context: A287302 A141915 A016133 * A155594 A077250 A356128
KEYWORD
nonn,easy
AUTHOR
David Nacin, Jun 07 2017
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)