A153340 Number of zig-zag paths from top to bottom of a rectangle of width 8 with n rows.

8, 14, 26, 48, 90, 168, 316, 592, 1114, 2090, 3932, 7382, 13884, 26076, 49032, 92110, 173170, 325360, 611618, 1149248, 2160212, 4059360, 7629882, 14338290, 26949004, 50644750, 95185300, 178883252, 336200648, 631835054, 1187485194, 2231705808

Offset: 1

Author

Joseph Myers, Dec 24 2008

Keywords

• easy
• nonn

Comments

Number of words of length n using an 8-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 (1,3,-2,-1).

Crossrefs

Column 8 of A220062.

Twice A090992.

Programs

Mathematica

LinearRecurrence[{1, 3, -2, -1}, {8, 14, 26, 48}, 32] (* Jean-François Alcover, Oct 08 2017 *)

Formula

G.f.: 2*x*(4+3*x-6*x^2-2*x^3)/((1-x)*(1-3*x^2-x^3)). - Colin Barker, May 10 2012