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A287830
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Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 7.
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0
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1, 10, 94, 886, 8350, 78694, 741646, 6989590, 65872894, 620814406, 5850821230, 55140648694, 519669123166, 4897584703270, 46156938822094, 435002788211926, 4099652849195710, 38636886795609094, 364130592557264686, 3431722880197818550, 32342028292009425694
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..20.
Index entries for linear recurrences with constant coefficients, signature (9, 4).
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FORMULA
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a(n) = 9*a(n-1) + 4*a(n-2), a(0)=1, a(1)=10.
G.f.: (-1 - x)/(-1 + 9*x + 4*x^2).
a(n) = ((1 - 11/sqrt(97))/2)*((9 - sqrt(97))/2)^n + ((1 + 11/sqrt(97))/2)*((9 + sqrt(97))/2)^n.
a(n) = A015580(n)+A015580(n+1). - R. J. Mathar, Oct 20 2019
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MATHEMATICA
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LinearRecurrence[{9, 4}, {1, 10}, 30]
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PROG
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(Python)
def a(n):
.if n in [0, 1]:
..return [1, 10][n]
.return 9*a(n-1)+4*a(n-2)
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CROSSREFS
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Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287831.
Sequence in context: A126633 A125422 A190988 * A259289 A163738 A190987
Adjacent sequences: A287827 A287828 A287829 * A287831 A287832 A287833
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KEYWORD
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nonn,easy
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AUTHOR
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David Nacin, Jun 02 2017
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STATUS
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approved
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