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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

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

Index entries for linear recurrences with constant coefficients, signature (9, 4).

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

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

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 02 2017

STATUS

approved

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Last modified February 24 12:47 EST 2021. Contains 341569 sequences. (Running on oeis4.)