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A287830 Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 7. 0
1, 10, 94, 886, 8350, 78694, 741646, 6989590, 65872894, 620814406, 5850821230, 55140648694, 519669123166, 4897584703270, 46156938822094, 435002788211926, 4099652849195710, 38636886795609094, 364130592557264686, 3431722880197818550, 32342028292009425694 (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
FORMULA
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
MATHEMATICA
LinearRecurrence[{9, 4}, {1, 10}, 30]
PROG
(Python)
def a(n):
.if n in [0, 1]:
..return [1, 10][n]
.return 9*a(n-1)+4*a(n-2)
CROSSREFS
Sequence in context: A126633 A125422 A190988 * A259289 A163738 A190987
KEYWORD
nonn,easy
AUTHOR
David Nacin, Jun 02 2017
STATUS
approved

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Last modified May 29 22:36 EDT 2024. Contains 372954 sequences. (Running on oeis4.)