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%I #17 Mar 03 2024 15:34:49
%S 10,18,34,64,122,232,444,848,1626,3112,5972,11442,21964,42106,80832,
%T 155010,297570,570760,1095620,2101752,4034252,7739690,14855342,
%U 28501710,54703004,104959000,201439550,386516750,741790648,1423365002,2731617694
%N Number of zig-zag paths from top to bottom of a rectangle of width 10 with n rows.
%C Number of words of length n using a 10 symbol alphabet where neighboring letters are neighbors in the alphabet. - _Andrew Howroyd_, Apr 17 2017
%H Joseph Myers, <a href="http://www.polyomino.org.uk/publications/2008/bmo1-2009-q1.pdf">BMO 2008--2009 Round 1 Problem 1---Generalisation</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 4, -3, -3, 1).
%F G.f.: 2*x*(5+4*x-12*x^2-6*x^3+3*x^4)/(1-x-4*x^2+3*x^3+3*x^4-x^5) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
%t LinearRecurrence[{1, 4, -3, -3, 1}, {10, 18, 34, 64, 122}, 31] (* _Jean-François Alcover_, Jul 01 2018 *)
%Y Column 10 of A220062.
%Y Twice A090994.
%K easy,nonn
%O 1,1
%A _Joseph Myers_, Dec 24 2008
%E G.f. proposed by Maksym Voznyy checked and corrected by _R. J. Mathar_, Sep 16 2009.