A153371 Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n rows whose color is that of the top right corner.
10, 36, 132, 488, 1812, 6744, 25132, 93720, 349620, 1304504, 4867884, 18166008, 67794100, 253006296, 944222892, 3523868888, 13151219892, 49080945144, 183172429612, 683608511160, 2551261090740, 9521434803224, 35534476025004
Offset: 1
Links
- Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation
- Index entries for linear recurrences with constant coefficients, signature (6, -9, 2).
Formula
Empirical: G.f. -2*x*(5-12*x+3*x^2) / ( (2*x-1)*(x^2-4*x+1) ) with a(n)= +6*a(n-1) -9*a(n-2) +2*a(n-3) and a(n) = (2^n+4*A001075(n+1))/3. - R. J. Mathar, Jun 16 2011