login
Number of 4 X n binary arrays with a path of adjacent 1's from top row to bottom row using only left, right, and downward steps.
1

%I #39 Feb 05 2025 09:20:21

%S 1,41,1041,22193,433801,8057625,144762849,2540882465,43840779353,

%T 746649798473,12587443678705,210491254232465,3496816762316713,

%U 57778098654714361,950391251581267073,15574198350636963201,254405750326548970361,4144508602760970898729,67361936661916258817937

%N Number of 4 X n binary arrays with a path of adjacent 1's from top row to bottom row using only left, right, and downward steps.

%C Unlike A069362, does not allow upward steps.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (36,-413,1642,-2536,1152).

%F G.f.: x*(1 + 5*x - 22*x^2 + 8*x^3)/((1 - 16*x)*(1 - 20*x + 93*x^2 - 154*x^3 + 72*x^4)). - _Pontus von Brömssen_, Feb 05 2025

%e For example, here is one such 4 X 4 array:

%e 0001

%e 1111

%e 1010

%e 1100

%e The following 4 X 5 array is a non-example, as there is no path using only left, right, and downward steps:

%e 10000

%e 10111

%e 11101

%e 00001

%Y Row 4 of A369892.

%Y Cf. A069362, A359576.

%K nonn,easy

%O 1,2

%A _Caleb Stanford_, Feb 05 2024

%E More terms from _Pontus von Brömssen_, Feb 05 2025