A287812 Number of octonary sequences of length n such that no two consecutive terms have distance 1.

1, 8, 50, 314, 1972, 12386, 77796, 488636, 3069120, 19277130, 121079578, 760500364, 4776699874, 30002433636, 188445170924, 1183623397912, 7434334035874, 46695023649050, 293291264969380, 1842161313673506, 11570608166423524, 72674945645197500

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 A357479 A133129

Adjacent sequences: A287809 A287810 A287811 * A287813 A287814 A287815

Keyword

nonn,easy

Author

David Nacin, Jun 02 2017

Status

approved