A287810 Number of septenary sequences of length n such that no two consecutive terms have distance 3.

1, 7, 41, 241, 1417, 8333, 49005, 288193, 1694833, 9967141, 58615749, 344713305, 2027224169, 11921900829, 70111496093, 412318635697, 2424804301985, 14260029486677, 83861794865077, 493182755657289, 2900358033942041, 17056713010658765, 100308808541321741

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (6, 1, -10).

Formula

For n>3, a(n) = 6*a(n-1) + a(n-2) - 10*a(n-3), a(0)=1, a(1)=7, a(2)=41, a(3)=241.

G.f.: (1 + x - 2*x^2 - 2*x^3)/(1 - 6*x - x^2 + 10*x^3).

Example

For n=2 the a(2) = 49-8 = 41 sequences contain every combination except these eight: 03, 30, 14, 41, 25, 52, 36, 63.

Mathematica

LinearRecurrence[{6, 1, -10}, {1, 7, 41, 241}, 40]

Prog

(Python)
def a(n):
.if n in [0, 1, 2, 3]:
..return [1, 7, 41, 241][n]
.return 6*a(n-1)+a(n-2)-10*a(n-3)

Crossrefs

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

Cf. A287804-A287819.

Sequence in context: A002315 A141813 A088165 * A292035 A108983 A115137

Adjacent sequences: A287807 A287808 A287809 * A287811 A287812 A287813

Keyword

nonn,easy

Author

David Nacin, Jun 01 2017

Status

approved