A287815 Number of octonary sequences of length n such that no two consecutive terms have distance 7.

1, 8, 62, 482, 3746, 29114, 226274, 1758602, 13667858, 106226618, 825593474, 6416514026, 49869159026, 387583197338, 3012297335522, 23411580532682, 181954847741906, 1414153417389434, 10990803008177474, 85420541561578922, 663888608980117298, 5159743512230294618

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (7, 6).

Formula

a(n) = 7*a(n-1) + 6*a(n-2), a(0)=1, a(1)=8.

G.f.: (-1 - x)/(-1 + 7 x + 6 x^2).

a(n) = A015564(n)+A015564(n+1). - R. J. Mathar, Oct 20 2019

Example

For n=2 the a(2) = 64 - 2 = 62 sequences contain every combination except these two: 07,70.

Mathematica

LinearRecurrence[{7, 6}, {1, 8}, 40]

Prog

(Python)
def a(n):
.if n in [0, 1]:
..return [1, 8][n]
.return 7*a(n-1)+6*a(n-2)

Crossrefs

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

Sequence in context: A125396 A163444 A190975 * A244831 A331235 A053095

Adjacent sequences: A287812 A287813 A287814 * A287816 A287817 A287818

Keyword

nonn,easy

Author

David Nacin, Jun 02 2017

Status

approved