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A287817 Number of nonary sequences of length n such that no two consecutive terms have distance 2. 0
1, 9, 67, 501, 3747, 28025, 209609, 1567743, 11725731, 87701095, 655949055, 4906086571, 36694443381, 274451368893, 2052723708275, 15353082914309, 114831408642039, 858866749063989, 6423783365292409, 48045861327359751, 359352839194448551, 2687733333725785179 (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 (8, -1, -23, 10, 1).

FORMULA

a(n) = 8*a(n-1) - 1*a(n-2) - 23*a(n-3) + 10*a(n-4) + a(n-5), a(0)=1, a(1)=9, a(2)=67, a(3)=501, a(4)=3747.

G.f: (-1 - x + 4 x^2 + 3 x^3 - 3 x^4)/(-1 + 8 x - x^2 - 23 x^3 + 10 x^4 + x^5).

EXAMPLE

For n=2 the a(2) = 81 - 14 = 67 sequences contain every combination except these fourteen: 02,20,13,31,24,42,35,53,46,64,57,75,68,86.

MATHEMATICA

LinearRecurrence[{8, -1, -23, 10, 1}, {1, 9, 67 , 501, 3747}, 40]

PROG

(Python)

def a(n):

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

..return [1, 9, 67 , 501, 3747][n]

.return 8*a(n-1)-a(n-2)-23*a(n-3)+10*a(n-4)+a(n-5)

CROSSREFS

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

Sequence in context: A163349 A016130 A115202 * A155592 A002051 A231192

Adjacent sequences:  A287814 A287815 A287816 * A287818 A287819 A287820

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 02 2017

STATUS

approved

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Last modified January 20 10:55 EST 2022. Contains 350472 sequences. (Running on oeis4.)