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 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(3n+2) = 2*a(3n+1). 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). FORMULA 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) EXAMPLE 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. 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 *) PROG (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

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Last modified October 23 18:36 EDT 2018. Contains 316529 sequences. (Running on oeis4.)