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A287829 Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 6. 0
1, 10, 92, 848, 7816, 72040, 663992, 6120008, 56408056, 519912520, 4792028792, 44168084168, 407096815096, 3752207504200, 34584061167992, 318760965520328, 2938016812018936, 27079673239211080, 249593092776937592, 2300497181470860488, 21203660818791619576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, the number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 5+k for k in {0,1,2,3,4} is given by a(n) = 9*a(n-1) + 2*k*a(n-2), a(0)=1, a(1)=10.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (9, 2).

FORMULA

a(n) = 9*a(n-1) + 2*a(n-2), a(0)=1, a(1)=10.

G.f.: (-1 - x)/(-1 + 9*x + 2*x^2).

a(n) = ((1 - 11/sqrt(89))/2)*((9 - sqrt(89))/2)^n + ((1 + 11/sqrt(89))/2)*((9 + sqrt(89))/2)^n.

a(n) = A015579(n)+A015579(n+1). - R. J. Mathar, Oct 20 2019

MATHEMATICA

LinearRecurrence[{9, 2}, {1, 10}, 30]

PROG

(Python)

def a(n):

.if n in [0, 1]:

..return [1, 10][n]

.return 9*a(n-1)+2*a(n-2)

CROSSREFS

Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287831.

Sequence in context: A037534 A120996 A190990 * A265242 A262173 A103944

Adjacent sequences:  A287826 A287827 A287828 * A287830 A287831 A287832

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 02 2017

STATUS

approved

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Last modified January 22 13:21 EST 2021. Contains 340362 sequences. (Running on oeis4.)