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A287827 Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 3. 0
1, 10, 86, 742, 6404, 55274, 477082, 4117804, 35541714, 306768722, 2647791524, 22853698754, 197255539962, 1702558017644, 14695170558994, 126837403201602, 1094762853302164, 9449150445514434, 81557794797885642, 703944119701429084, 6075903902137709074 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (9, -1, -20, 10).

FORMULA

For n>4, a(n) = 9*a(n-1) - a(n-2) - 20*a(n-3) + 10*a(n-4), a(0)=1, a(1)=10, a(2)=86, a(3)=742, a(4)=6404.

G.f.: (-1 - x + 3*x^2 + 2*x^3 - 2*x^4)/(-1 + 9*x - x^2 - 20*x^3 + 10*x^4).

MATHEMATICA

LinearRecurrence[{9, -1, -20, 10}, {1, 10, 86, 742, 6404}, 30]

PROG

(Python)

def a(n):

.if n in [0, 1, 2, 3, 4]:

..return [1, 10, 86, 742, 6404][n]

.return 9*a(n-1)-a(n-2)-20*a(n-3)+10*a(n-4)

CROSSREFS

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

Sequence in context: A184122 A228123 A163412 * A321853 A264174 A218894

Adjacent sequences:  A287824 A287825 A287826 * A287828 A287829 A287830

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 02 2017

STATUS

approved

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Last modified March 2 06:37 EST 2021. Contains 341744 sequences. (Running on oeis4.)