A287818 Number of nonary sequences of length n such that no two consecutive terms have distance 3.

1, 9, 69, 531, 4089, 31491, 242529, 1867851, 14385369, 110789811, 853254609, 6571393371, 50609994249, 389776014531, 3001884188289, 23119197549291, 178053936060729, 1371293449053651, 10561101680875569, 81336980637343611, 626421808927336809, 4824426473972595171

Offset: 0

Author

David Nacin, Jun 02 2017

Keywords

• nonn
• easy

Examples

			For n=2 the a(2) = 81 - 12 = 69 sequences contain every combination except these twelve: 03,30,14,41,25,52,36,63,47,74,58,85.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (9, -10).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{9, -10}, {1, 9, 69}, 40]

Python

def a(n):
 if n in [0, 1, 2]:
  return [1, 9, 69][n]
 return 9*a(n-1)-10*a(n-2)

Formula

For n>2, a(n) = 9*a(n-1) - 10*a(n-2), a(0)=1, a(1)=9, a(2)=69.

G.f.: (1 - 2 x^2)/(1 - 9 x + 10 x^2).

For n>0, a(n)=(1/5)(3 - 18/sqrt(41))*((9 - sqrt(41))/2)^n + (1/5)(3 + 18/sqrt(41))*((9 + sqrt(41))/2)^n.

a(n) = A178869(n+1)-2*A178869(n-1). - R. J. Mathar, Oct 20 2019