cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A164315 Number of binary strings of length n with no substrings equal to 000 or 011.

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%I A164315 #20 Nov 01 2024 12:45:13
%S A164315 1,2,4,6,9,13,18,25,34,46,62,83,111,148,197,262,348,462,613,813,1078,
%T A164315 1429,1894,2510,3326,4407,5839,7736,10249,13578,17988,23830,31569,
%U A164315 41821,55402,73393,97226,128798,170622,226027,299423,396652,525453,696078,922108
%N A164315 Number of binary strings of length n with no substrings equal to 000 or 011.
%H A164315 Alois P. Heinz, <a href="/A164315/b164315.txt">Table of n, a(n) for n = 0..5000</a> (first 500 terms from R. H. Hardin)
%H A164315 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 A164315 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1).
%F A164315 G.f.: (x^2+x+1)/((x-1)*(x^3+x^2-1)). - _R. J. Mathar_, Nov 28 2011
%e A164315 All solutions for N=6
%e A164315 001001 001010 010010 010100 010101 100100 100101 101001 101010 110010
%e A164315 110100 110101 111001 111010 111100 111101 111110 111111
%t A164315 CoefficientList[Series[(x^2 + x + 1)/((x - 1) (x^3 + x^2 - 1)), {x, 0, 44}], x] (* _Michael De Vlieger_, Oct 11 2017 *)
%Y A164315 Cf. A171861 (essentially the same sequence).
%K A164315 nonn,easy
%O A164315 0,2
%A A164315 _R. H. Hardin_, Aug 12 2009
%E A164315 Edited by _Alois P. Heinz_, Oct 11 2017