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A287816 Number of nonary sequences of length n such that no two consecutive terms have distance 1. 0
1, 9, 65, 471, 3413, 24733, 179233, 1298853, 9412437, 68209395, 494295113, 3582023557, 25957960001, 188110345129, 1363185009337, 9878634630295, 71587804656589, 518777540353453, 3759441118026705, 27243657291488469, 197427447142906157, 1430703538380753875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (9, -11, -15, 19, 1).

FORMULA

a(n) = 9*a(n-1) - 11*a(n-2) - 15*a(n-3) + 19*a(n-4) + a(n-5), a(0)=1, a(1)=9, a(2)=65, a(3)=471, a(4)=3413.

G.f: (-1 + 5 x^2 - 5 x^4)/(-1 + 9 x - 11 x^2 - 15 x^3 + 19 x^4 + x^5).

EXAMPLE

For n=2 the a(2) = 81 - 16 = 65 sequences contain every combination except these sixteen: 01,10,12,21,23,32,34,43,45,54,56,65,67,76,78,87.

MATHEMATICA

LinearRecurrence[{9, -11, -15, 19, 1}, {1, 9, 65 , 471, 3413}, 40]

PROG

(Python)

def a(n):

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

..return [1, 9, 65 , 471, 3413][n]

.return 9*a(n-1)-11*a(n-2)-15*a(n-3)+19*a(n-4)+a(n-5)

CROSSREFS

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

Sequence in context: A127534 A037548 A238275 * A036731 A020234 A154996

Adjacent sequences:  A287813 A287814 A287815 * A287817 A287818 A287819

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 02 2017

STATUS

approved

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Last modified June 24 01:07 EDT 2021. Contains 345404 sequences. (Running on oeis4.)