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A287836 Number of words over the alphabet {0,1,...,10} such that no two consecutive terms have distance 5. 0
1, 11, 109, 1081, 10721, 106329, 1054553, 10458881, 103729441, 1028771337, 10203182953, 101193470929, 1003620008177, 9953736259545, 98719500126905, 979083577381409, 9710388021269185, 96306012787788969, 955147011506293513, 9472989143467878769, 93951530216004879761 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (10, 1, -18).

FORMULA

For n>3, a(n) = 10*a(n-1) + a(n-2) - 18*a(n-3), a(0)=1, a(1)=11, a(2)=109, a(3)=1081.

G.f.: (1 + x - 2*x^2 - 2*x^3)/(1 - 10*x - x^2 + 18*x^3).

MATHEMATICA

LinearRecurrence[{10, 1, -18}, {1, 11, 109, 1081}, 20]

PROG

(Python)

def a(n):

.if n in [0, 1, 2, 3]:

..return [1, 11, 109, 1081][n]

.return 10*a(n-1) + a(n-2) - 18*a(n-3)

CROSSREFS

Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287839.

Sequence in context: A165149 A048346 A054320 * A124290 A094703 A324355

Adjacent sequences:  A287833 A287834 A287835 * A287837 A287838 A287839

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 07 2017

STATUS

approved

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Last modified March 25 08:15 EDT 2019. Contains 321469 sequences. (Running on oeis4.)