login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of length n 0..2 arrays with no pair in any consecutive three terms totalling exactly 2.
1

%I #28 Dec 31 2023 11:16:23

%S 1,3,6,8,12,18,26,38,56,82,120,176,258,378,554,812,1190,1744,2556,

%T 3746,5490,8046,11792,17282,25328,37120,54402,79730,116850,171252,

%U 250982,367832,539084,790066,1157898,1696982,2487048,3644946,5341928,7828976,11473922

%N Number of length n 0..2 arrays with no pair in any consecutive three terms totalling exactly 2.

%C Also, number of length n ternary words with no pair of equal consecutive letters and avoiding the subwords 010, 101, 020, 202. - _Miquel A. Fiol_, Dec 22 2023

%H Alois P. Heinz, <a href="/A245989/b245989.txt">Table of n, a(n) for n = 0..2000</a> (210 terms from R. H. Hardin)

%F a(n) = a(n-1) + a(n-3) for n>=5.

%F G.f.: (x^4 + x^3 + 3*x^2 + 2*x + 1) / (1 - x - x^3). - _Colin Barker_, Nov 05 2018

%e Some solutions for n=12:

%e 0 1 0 1 1 0 2 2 0 2 0 2 0 0 0 1

%e 0 2 1 2 0 0 1 2 1 1 0 2 0 0 1 2

%e 0 2 0 2 0 1 2 1 0 2 0 2 0 0 0 2

%e 0 2 0 1 0 0 2 2 0 2 1 1 1 1 0 1

%e 0 1 1 2 0 0 2 2 0 2 0 2 0 0 0 2

%e 0 2 0 2 1 1 2 1 1 1 0 2 0 0 0 2

%e 0 2 0 2 0 0 1 2 0 2 0 2 0 0 1 2

%e 0 2 0 2 0 0 2 2 0 2 0 2 0 0 0 2

%e 0 1 1 2 1 1 2 1 0 2 0 1 1 0 0 1

%e 0 2 0 1 0 0 2 2 0 2 0 2 0 0 0 2

%e 0 2 0 2 0 0 2 2 0 1 1 2 0 0 0 2

%e 0 2 0 2 1 0 1 1 0 2 0 1 0 0 1 2

%t gf=(x^4 + x^3 + 3*x^2 + 2*x + 1) / (1 - x - x^3);Table[SeriesCoefficient[gf, {x, 0, n}], {n, 0, 40}] (* _James C. McMahon_, Dec 30 2023 *)

%Y Column 2 of A245995.

%K nonn,easy

%O 0,2

%A _R. H. Hardin_, Aug 09 2014

%E Edited by _Alois P. Heinz_, Dec 30 2023