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

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

Offset: 1

Author

Joseph Myers, Dec 24 2008

Keywords

• easy
• nonn

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

• Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation
• Index entries for linear recurrences with constant coefficients, signature (0, 6, 0, -9, 0, 2).

Crossrefs

Column 11 of A220062.

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

Programs

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[iJean-François Alcover, Jul 01 2018, after Alois P. Heinz *)

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