A287808 Number of septenary sequences of length n such that no two consecutive terms have distance 1.

1, 7, 37, 197, 1049, 5587, 29757, 158491, 844153, 4496123, 23947233, 127547675, 679344041, 3618320227, 19271886609, 102645866251, 546712113769, 2911896468083, 15509334488577, 82605772190267, 439974623297369, 2343391557436483, 12481365289466289

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