# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a263656 Showing 1-1 of 1 %I A263656 #23 Oct 08 2017 09:56:55 %S A263656 0,0,4,6,12,30,70,168,412,1014,2514,6270,15702,39468,99516,251586, %T A263656 637500,1618638,4117102,10488684,26758762,68354250,174810354, %U A263656 447533586,1146836662,2941443180,7550434480,19395863358,49859516292,128252962434,330101861850 %N A263656 Number of length-2n central circular binary strings without zigzags (see reference for precise definition). %C A263656 See page 6 in the reference. %C A263656 A zigzag is a substring which is either 010 or 101. The central binary strings are those that contain an equal number of 0's and 1's. %H A263656 Andrew Howroyd, Table of n, a(n) for n = 0..100 %H A263656 E. Munarini and N. Z. Salvi, Circular Binary Strings without Zigzags, Integers: Electronic Journal of Combinatorial Number Theory 3 (2003), #A19. %F A263656 a(n) = (1/n)*(3*(n-1)*a(n-1) - 4*(n-4)*a(n-2) + (7*n-27)*a(n-3) - 6*a(n-4) + (7*n-37)*a(n-5) - 3*(n-6)*a(n-6)) for n >= 6. - _Andrew Howroyd_, Feb 26 2017 %e A263656 For n=3 the 6 strings are 000111, 001110, 011100, 111000, 110001, 100011. %t A263656 a[n_ /; n < 6] := {0, 0, 4, 6, 12, 30}[[n + 1]]; a[n_] := a[n] = (-(3*(n - 6)*a[n - 6]) + (7*n - 37)*a[n - 5] - 6*a[n - 4] + (7*n - 27)*a[n - 3] - 4*(n - 4)*a[n - 2] + 3*(n - 1)*a[n - 1])/n; %t A263656 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Oct 08 2017, after _Andrew Howroyd_ *) %Y A263656 Main diagonal of A263655. %Y A263656 Cf. A007039, A263657, A263658, A263659. %K A263656 nonn %O A263656 0,3 %A A263656 _Felix Fröhlich_, Oct 23 2015 %E A263656 corrected a(1) and a(17)-a(30) from _Andrew Howroyd_, Feb 26 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE