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

Author

David Nacin, Jun 02 2017

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

Python

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

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