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A287825
Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 1.
15
1, 10, 82, 674, 5540, 45538, 374316, 3076828, 25291120, 207889674, 1708825732, 14046322404, 115458919774, 949057110644, 7801124426174, 64124215108032, 527092600834054, 4332631742719370, 35613662169258228, 292739611493034596, 2406281042646218328
OFFSET
0,2
FORMULA
For n>5, a(n) = 9*a(n-1) - 4*a(n-2) - 21*a(n-3) + 9*a(n-4) + 5*a(n-5), a(0)=1, a(1)=10, a(2)=82, a(3)=674, a(4)=5540, a(5)=45538.
G.f.: (-1 - x + 4*x^2 + 3*x^3 - 3*x^4 - x^5)/(-1 + 9*x - 4*x^2 - 21*x^3 + 9*x^4 + 5*x^5).
MATHEMATICA
LinearRecurrence[{9, -4, -21, 9, 5}, {1, 10, 82, 674, 5540, 45538}, 40]
PROG
(Python)
def a(n):
if n in [0, 1, 2, 3, 4, 5]:
return [1, 10, 82, 674, 5540, 45538][n]
return 9*a(n-1) - 4*a(n-2) - 21*a(n-3) + 9*a(n-4) + 5*a(n-5)
KEYWORD
nonn,easy
AUTHOR
David Nacin, Jun 02 2017
STATUS
approved