A287805 Number of quinary sequences of length n such that no two consecutive terms have distance 2.

1, 5, 19, 73, 281, 1083, 4175, 16097, 62065, 239307, 922711, 3557761, 13717913, 52893147, 203943935, 786361409, 3032030689, 11690820555, 45077144455, 173807214241, 670161078089, 2583988659867, 9963272432111, 38416111919777, 148123788152017, 571131629935179

Offset: 0

Author

David Nacin, Jun 01 2017

Keywords

• nonn
• easy

Examples

			For n=2 the a(2)=19=25-6 sequences contain every combination except these six: 02,20,13,31,24,42.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4, 1, -6).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{4, 1, -6}, {1, 5, 19, 73}, 40]

Python

def a(n):
 if n in [0,1,2,3]:
  return [1,5,19,73][n]
 return 4*a(n-1)+a(n-2)-6*a(n-3)

Formula

For n>0, a(n) = 4*a(n-1) + a(n-2) - 6*a(n-3), a(1)=5, a(2)=19, a(3)=73.

G.f.: (1 + x - 2*x^2 - 2*x^3)/(1 - 4*x - x^2 + 6*x^3).