A287814 Number of octonary sequences of length n such that no two consecutive terms have distance 3.

1, 8, 54, 366, 2482, 16834, 114178, 774426, 5252642, 35626714, 241642738, 1638972746, 11116542082, 75399367194, 511405842898, 3468675479466, 23526734684322, 159573084361274, 1082324835734258, 7341006503296586, 49791314679463362, 337715954398900954

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (7, 0, -10).

Formula

For n>3, a(n) = 7*a(n-1) - 10*a(n-3), a(0)=1, a(1)=8, a(2)=54, a(3)=366.

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

Example

For n=2 the a(2) = 64 - 10 = 54 sequences contain every combination except these ten: 03,30,14,41,25,52,36,63,47,74.

Mathematica

LinearRecurrence[{7, 0, -10}, {1, 8, 54, 366}, 40]

Prog

(Python)
def a(n):
.if n in [0, 1, 2, 3]:
..return [1, 8, 54, 366][n]
.return 7*a(n-1)-10*a(n-3)

Crossrefs

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

Sequence in context: A208310 A154235 A289796 * A201640 A263885 A002775

Adjacent sequences: A287811 A287812 A287813 * A287815 A287816 A287817

Keyword

nonn,easy

Author

David Nacin, Jun 02 2017

Status

approved