A163706 Number of n X 4 binary arrays with all 1s connected, a path of 1s from left column to lower right corner, and no 1 having more than two 1s adjacent.

1, 11, 63, 259, 896, 2821, 8515, 24940, 70944, 196626, 534162, 1430008, 3786133, 9937397, 25902833, 67151065, 173338487, 445930356, 1144130515, 2929289696, 7487194973, 19111652812, 48732676423, 124159731735, 316122564155, 804460022994, 2046327745604, 5203616238664

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (11,-52,140,-237,246,-92,-164,329,-268,44,143,-158,58,30,-44,14,5,-6,1,1).

Formula

G.f.: x*(1 - 6*x^2 - 2*x^3 + 20*x^4 - 26*x^5 + 133*x^6 - 412*x^7 + 353*x^8 - 8*x^9 - 62*x^10 + 230*x^11 - 218*x^12 + 42*x^13 + 86*x^14 - 132*x^15 + 36*x^16 + 60*x^17 - 19*x^18 + 2*x^19 + 4*x^20 - 2*x^21)/((1 - x)^3*(1 - 2*x - x^4)*(1 - 2*x + x^2 - x^3 - x^4)^2*(1 - 2*x - x^2 - 2*x^4 - x^5)). - Andrew Howroyd, Dec 23 2025

Example

All solutions for n=2:
...0.0.0.0...0.0.0.1...1.0.0.0...1.0.0.1...1.1.0.0...1.1.0.1...1.1.1.0
...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...0.1.1.1...0.1.1.1...0.0.1.1
------
...1.1.1.0...1.1.1.1...1.1.1.1...0.1.1.1
...1.0.1.1...0.0.0.1...1.0.0.1...1.1.0.1

Crossrefs

Row 4 of A391823.

Sequence in context: A298046 A120723 A053367 * A180763 A362164 A357959

Adjacent sequences: A163703 A163704 A163705 * A163707 A163708 A163709

Keyword

nonn,easy

Author

R. H. Hardin, Aug 03 2009

Extensions

a(22) onward from Andrew Howroyd, Dec 23 2025

Status

approved