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A287812 Number of octonary sequences of length n such that no two consecutive terms have distance 1. 0
1, 8, 50, 314, 1972, 12386, 77796, 488636, 3069120, 19277130, 121079578, 760500364, 4776699874, 30002433636, 188445170924, 1183623397912, 7434334035874, 46695023649050, 293291264969380, 1842161313673506, 11570608166423524, 72674945645197500 (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 (7, -3, -10, 3).

FORMULA

For n>4, a(n) = 7*a(n-1) - 3*a(n-2) - 10*a(n-3) + 3*a(n-2), a(0)=1, a(1)=8, a(2)=50, a(3)=314, a(4)=1972.

G.f.: (-1 - x + 3 x^2 + 2 x^3 - x^4)/(-1 + 7 x - 3 x^2 - 10 x^3 + 3 x^4).

EXAMPLE

For n=2 the a(2) = 64 - 14 = 50 sequences contain every combination except these fourteen: 01,10,12,21,23,32,34,43,45,54,56,65,67,76.

MATHEMATICA

LinearRecurrence[{7, -3, -10, 3}, {1, 8, 50, 314, 1972}, 40]

PROG

(Python)

def a(n):

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

..return [1, 8, 50, 314, 1972][n]

.return 7*a(n-1)-3*a(n-2)-10*a(n-3)+3*a(n-4)

CROSSREFS

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

Sequence in context: A061801 A240050 A221478 * A180029 A133129 A103458

Adjacent sequences:  A287809 A287810 A287811 * A287813 A287814 A287815

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 02 2017

STATUS

approved

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Last modified May 25 10:01 EDT 2020. Contains 334592 sequences. (Running on oeis4.)