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A287808 Number of septenary sequences of length n such that no two consecutive terms have distance 1. 0
1, 7, 37, 197, 1049, 5587, 29757, 158491, 844153, 4496123, 23947233, 127547675, 679344041, 3618320227, 19271886609, 102645866251, 546712113769, 2911896468083, 15509334488577, 82605772190267, 439974623297369, 2343391557436483, 12481365289466289 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (7, -8, -6, 6).

FORMULA

For n>4, a(n) =  7*a(n-1) - 8*a(n-2) - 6*a(n-3) + 6*a(n-4), a(1)=7, a(2)=37, a(3)=197, a(4)=1049.

G.f.: (1-4*x^2+2*x^4)/(1-7*x+8*x^2+6*x^3-6*x^4).

EXAMPLE

For n=2 the a(2)=37=49-12 sequences contain every combination except these twelve: 01,10,12,21,23,32,34,43,45,54,56,65.

MATHEMATICA

LinearRecurrence[{7, -8, -6, 6}, {1, 7, 37, 197, 1049}, 40]

PROG

(Python)

def a(n):

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

..return [1, 7, 37, 197, 1049][n]

.return 7*a(n-1)-8*a(n-2)-6*a(n-3)+6*a(n-4)

CROSSREFS

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

Sequence in context: A085640 A196805 A069378 * A117130 A002807 A124610

Adjacent sequences:  A287805 A287806 A287807 * A287809 A287810 A287811

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 01 2017

STATUS

approved

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Last modified November 18 00:38 EST 2017. Contains 294837 sequences.