A287813 - OEIS

A287813

Number of octonary sequences of length n such that no two consecutive terms have distance 2.

1, 8, 52, 340, 2224, 14548, 95164, 622504, 4072036, 26636740, 174241072, 1139777284, 7455717772, 48770692552, 319027694548, 2086881784180, 13651089405616, 89296980486772, 584125595190556, 3820988224873576, 24994540788543364, 163498820845182820

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OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (7, -3).

FORMULA

For n>2, a(n) = 7*a(n-1) - 3*a(n-2), a(0)=1, a(1)=8, a(2)=52.

G.f.: (1 + x - x^2)/(1 - 7 x + 3 x^2).

a(n) = A190972(n) + A190972(n+1) - A190972(n-1). - R. J. Mathar, Oct 20 2019

EXAMPLE

For n=2 the a(2) = 64 - 12 = 52 sequences contain every combination except these twelve: 02,20,13,31,24,42,35,53,46,64,57,75.

MATHEMATICA

LinearRecurrence[{7, -3}, {1, 8, 52}, 40]

PROG

(Python)

def a(n):

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

..return [1, 8, 52][n]

.return 7*a(n-1)-3*a(n-2)

CROSSREFS

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

Sequence in context: A016129 A006631 A205218 * A126503 A155590 A130153

Adjacent sequences: A287810 A287811 A287812 * A287814 A287815 A287816

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 02 2017

STATUS

approved