A164317 - OEIS

%I #43 Nov 18 2024 07:07:32

%S 1,2,4,5,6,7,9,11,13,16,20,24,29,36,44,53,65,80,97,118,145,177,215,

%T 263,322,392,478,585,714,870,1063,1299,1584,1933,2362,2883,3517,4295,

%U 5245,6400,7812,9540,11645,14212,17352,21185,25857,31564,38537,47042,57421

%N Number of binary strings of length n with no substrings equal to 000, 010, or 111.

%H Alois P. Heinz, <a href="/A164317/b164317.txt">Table of n, a(n) for n = 0..5000</a> (first 500 terms from R. H. Hardin)

%H Lukas Fleischer and Jeffrey Shallit, <a href="https://arxiv.org/abs/1911.12464">Words With Few Palindromes, Revisited</a>, arXiv:1911.12464 [cs.FL], 2019.

%H Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.

%H N. H. Bong, C. Dalfó, M. A. Fiol, and D. Závacká, <a href="https://doi.org/10.1007/s40590-024-00691-8">Some inner metric parameters of a digraph: iterated line digraphs and integer sequences</a>, Bol. Soc. Mat. Mex. 31 (2025), 13.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1).

%F G.f.: -(x^2+x+1)*(x^3+2*x^2+x+1)/(x^4+x^3-1). - _R. J. Mathar_, Nov 28 2011

%e All solutions for N=8

%e 00110110 00110011 10110110 10110011 10011001 10011011 01100110 01101100

%e 01101101 11001100 11001101 11011001 11011011

%t CoefficientList[Series[-(x^2 + x + 1) (x^3 + 2 x^2 + x + 1)/(x^4 + x^3 - 1), {x, 0, 50}], x] (* _Michael De Vlieger_, Feb 17 2020 *)

%K nonn,easy,changed

%O 0,2

%A _R. H. Hardin_, Aug 12 2009

%E Edited by _Alois P. Heinz_, Oct 11 2017