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A153368 Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows. 5
11, 20, 38, 72, 138, 264, 508, 976, 1882, 3624, 6996, 13488, 26054, 50264, 97124, 187440, 362250, 699240, 1351492, 2609008, 5042950, 9735768, 18818772, 36332016, 70229066, 135588200, 262091348, 506012592, 978124038, 1888445784, 3650380228 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Heuristically, a(n) = +6*a(n-2) -9*a(n-4) +2*a(n-6). - R. J. Mathar, Jun 16 2011

Number of words of length n using a 11 symbol alphabet where neighboring letters are neighbors in the alphabet. - Andrew Howroyd, Apr 17 2017

LINKS

Table of n, a(n) for n=1..31.

Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation

FORMULA

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

a(n) = A153369(n) + A153370(n). - Andrew Howroyd, Apr 17 2017

MATHEMATICA

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]]];

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

Array[a, 31] (* Jean-Fran├žois Alcover, Jul 01 2018, after Alois P. Heinz *)

CROSSREFS

Column 11 of A220062.

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

Sequence in context: A109376 A100038 A160843 * A068600 A158235 A158245

Adjacent sequences:  A153365 A153366 A153367 * A153369 A153370 A153371

KEYWORD

easy,nonn

AUTHOR

Joseph Myers, Dec 24 2008

STATUS

approved

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Last modified December 14 19:27 EST 2019. Contains 329987 sequences. (Running on oeis4.)