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A287838 Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 8. 1
1, 11, 115, 1205, 12625, 132275, 1385875, 14520125, 152130625, 1593906875, 16699721875, 174966753125, 1833166140625, 19206495171875, 201230782421875, 2108340300078125, 22089556912890625, 231437270629296875, 2424820490857421875, 25405391261720703125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, the number of sequences on {0,1,...,10} such that no two consecutive terms have distance 6+k for k in {0,1,2,3,4} has generating function (-1 - x)/(-1 + 10*x + (2*k+1)*x^2).

LINKS

Colin Barker, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (10,5).

FORMULA

For n > 2, a(n) = 10*a(n-1) + 5*a(n-2), a(0)=1, a(1)=11, a(2)=115.

G.f.: (-1 - x)/(-1 + 10*x + 5*x^2).

a(n) = (((5-sqrt(30))^n*(-6+sqrt(30)) + (5+sqrt(30))^n*(6+sqrt(30)))) / (2*sqrt(30)). - Colin Barker, Nov 25 2017

MATHEMATICA

LinearRecurrence[{10, 5}, {1, 11, 115}, 20]

PROG

(Python)

def a(n):

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

..return [1, 11, 115][n]

.return 10*a(n-1) + 5*a(n-2)

(PARI) Vec((1 + x) / (1 - 10*x - 5*x^2) + O(x^40)) \\ Colin Barker, Nov 25 2017

CROSSREFS

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

Sequence in context: A332729 A160465 A125446 * A271477 A076554 A173616

Adjacent sequences:  A287835 A287836 A287837 * A287839 A287840 A287841

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 07 2017

STATUS

approved

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)