The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A069429 Half the number of 3 X n binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row. 94
 3, 16, 84, 440, 2304, 12064, 63168, 330752, 1731840, 9068032, 47480832, 248612864, 1301753856, 6816071680, 35689414656, 186872201216, 978475548672, 5123364487168, 26826284728320, 140464250421248, 735480363614208, 3851025180000256, 20164229625544704, 105581277033267200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (6,-4). FORMULA Empirical G.f.: x*(3-2*x)/(1-6*x+4*x^2).  - Colin Barker, Feb 22 2012 Empirical: a(n) = 3*A084326(n) - 2*A084326(n-1). - R. J. Mathar, Nov 09 2018 From Andrew Howroyd, Oct 27 2020: (Start) The above conjectures are true and follow from formulas given in A069361 and A069396. a(n) = (8^n)/2 - A069361(n) + A069396(n). a(n) = 2^(n-1)*Fibonacci(2*n+2) = A084326(n+1)/2. (End) EXAMPLE From Andrew Howroyd, Oct 27 2020: (Start) Some of the 2*a(2) = 32 arrays are:   0 0   0 0   0 0   0 1   0 1   0 0   0 1   0 0   0 1   1 1   1 0   1 0   1 1   1 0   1 1   1 1   1 1   1 1   0 1   0 0   1 1 (End) MATHEMATICA LinearRecurrence[{6, -4}, {3, 16}, 100] (* Jean-François Alcover, Nov 01 2020 *) PROG (PARI) Vec((3 - 2*x)/(1 - 6*x + 4*x^2) + O(x^30)) \\ Andrew Howroyd, Oct 27 2020 (PARI) a(n) = 2^(n-1)*fibonacci(2*n+2) \\ Andrew Howroyd, Oct 27 2020 CROSSREFS Cf. 2 X n A000079, n X 1 A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452. Cf. A084326. Sequence in context: A041707 A037584 A030983 * A275402 A026131 A026160 Adjacent sequences:  A069426 A069427 A069428 * A069430 A069431 A069432 KEYWORD nonn,easy AUTHOR R. H. Hardin, Mar 22 2002 EXTENSIONS Terms a(21) and beyond from Andrew Howroyd, Oct 27 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 25 09:48 EST 2021. Contains 340416 sequences. (Running on oeis4.)