A153369 Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows whose color is that of the top right corner.

6, 10, 20, 36, 72, 132, 264, 488, 976, 1812, 3624, 6744, 13488, 25132, 50264, 93720, 187440, 349620, 699240, 1304504, 2609008, 4867884, 9735768, 18166008, 36332016, 67794100, 135588200, 253006296, 506012592, 944222892, 1888445784, 3523868888

Offset

1,1

Links

Table of n, a(n) for n=1..32.

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).

Formula

Empirically, g.f. -2*x*(3+5*x-8*x^2-12*x^3+3*x^4+3*x^5) / ( (2*x^2-1)*(x^4-4*x^2+1) ) with a(n)= +6*a(n-2) -9*a(n-4) +2*a(n-6). - R. J. Mathar, Jun 16 2011

Mathematica

LinearRecurrence[{0, 6, 0, -9, 0, 2}, {6, 10, 20, 36, 72, 132}, 40] (* Harvey P. Dale, Sep 25 2024 *)

Crossrefs

A153368, A153370, A153371, A153372, A153373

Sequence in context: A117348 A117349 A362183 * A107981 A065758 A348838

Adjacent sequences: A153366 A153367 A153368 * A153370 A153371 A153372

Keyword

easy,nonn

Author

Joseph Myers, Dec 24 2008

Status

approved