A284840 Number of quinternary strings avoiding consecutive digits i,i+1 and i,i+2.

1, 5, 18, 63, 224, 799, 2846, 10132, 36073, 128438, 457304, 1628224, 5797263, 20641062, 73492179, 261667749, 931663897, 3317174627, 11810748015, 42051982296, 149725420655, 533095002085, 1898076358760, 6758070980980, 24062005289281, 85672390859855

Offset: 0

Author

Alois P. Heinz, Apr 03 2017

Keywords

• nonn
• easy

Examples

			a(2) = 18: 00, 03, 04, 10, 11, 14, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-7,8,-5,1).

Crossrefs

Cf. A277668.

Programs

Maple

a:= n->(<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>,
         <0|0|0|0|1>, <1|-5|8|-7|5>>^n)[5$2]:
seq(a(n), n=0..30);

Formula

G.f.: -1/(x^5-5*x^4+8*x^3-7*x^2+5*x-1).