A225879 Number of n-length words w over ternary alphabet {1,2,3} such that for every prefix z of w we have 0<=#(z,1)-#(z,2)<=2 and 0<=#(z,2)-#(z,3)<=2 and #(z,x) gives the number of occurrences of letter x in z.

1, 1, 2, 3, 7, 14, 23, 51, 102, 167, 371, 742, 1215, 2699, 5398, 8839, 19635, 39270, 64303, 142843, 285686, 467799, 1039171, 2078342, 3403199, 7559883, 15119766, 24757991, 54997523, 109995046, 180112335, 400102427, 800204854, 1310302327, 2910712035, 5821424070

Offset: 0

Author

Jon Perry, May 19 2013

Keywords

• nonn
• easy

Examples

			For n=6 the 23 words are: 112121, 112123, 112132, 112211, 112213, 112231, 112233, 112312, 112321, 112323, 121121, 121123, 121132, 121211, 121213, 121231, 121233, 121312, 121321, 121323, 123112, 123121 and 123123.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,7,0,0,2).

Crossrefs

Cf. A015555 (trisection)

Programs

JavaScript

function countOK(arr) {
var i,c=[0,0,0];
for (i=0;i=c[1] && c[0]-c[1]<=2 && c[1]>=c[2] && c[1]-c[2]<=2) return true; else return false;
}
x=new Array();
x[0]=new Array();
x[0][0]=[1];
document.write(x[0].length+", ");
for (i=1;i<21;i++) {
x[i]=new Array();
xc=0;
for (j=0;j
				

Maple

a:= n-> (<<0|1>, <2|7>>^iquo(n, 3, 'r').
        [<<1, 3>>, <<1, 7>>, <<2, 14>>][r+1])[1, 1]:
seq(a(n), n=0..50); # Alois P. Heinz, May 20 2013

Mathematica

LinearRecurrence[{0,0,7,0,0,2},{1,1,2,3,7,14},40] (* Harvey P. Dale, Mar 06 2015 *)

Formula

a(3n+2) = 2*a(3n+1).

From Alois P. Heinz, May 20 2013: (Start)

G.f.: (x-1)*(4*x^2+2*x+1) / (2*x^6+7*x^3-1).

a(n) = 7*a(n-3) + 2*a(n-6) for n>5. (End)