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A153368 Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows. 5

%I

%S 11,20,38,72,138,264,508,976,1882,3624,6996,13488,26054,50264,97124,

%T 187440,362250,699240,1351492,2609008,5042950,9735768,18818772,

%U 36332016,70229066,135588200,262091348,506012592,978124038,1888445784,3650380228

%N Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows.

%C Heuristically, a(n) = +6*a(n-2) -9*a(n-4) +2*a(n-6). - _R. J. Mathar_, Jun 16 2011

%C Number of words of length n using a 11 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>

%F Empirical G.f.: x*(11+20*x-28*x^2-48*x^3+9*x^4+12*x^5)/((1-2*x^2)*(1-4*x^2+x^4)). - _Colin Barker_, Apr 17 2012

%F a(n) = A153369(n) + A153370(n). - _Andrew Howroyd_, Apr 17 2017

%t b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0, Sum[b[n - 1, j, k], {j, 1, k}], If[i>1, b[n-1, i-1, k], 0] + If[i<k, b[n-1, i+1, k], 0]]];

%t a[n_] := b[n, 0, 11];

%t Array[a, 31] (* _Jean-Fran├žois Alcover_, Jul 01 2018, after _Alois P. Heinz_ *)

%Y Column 11 of A220062.

%Y Cf. A153369, A153370, A153371, A153372 (bisection), A153373.

%K easy,nonn

%O 1,1

%A _Joseph Myers_, Dec 24 2008

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Last modified January 28 03:49 EST 2020. Contains 331317 sequences. (Running on oeis4.)