A163735 Number of n X 4 binary arrays with all 1s connected, all corners 1, and no 1 having more than two 1s adjacent.

1, 2, 9, 13, 29, 87, 299, 917, 2589, 7059, 19075, 51111, 135445, 355377, 925723, 2398807, 6190289, 15920685, 40835851, 104520403, 267077847, 681561299, 1737491201, 4425749143, 11266099211, 28664410623, 72902498443, 185356982381, 471163733305, 1197440776399

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,-13,14,-7,-9,16,-8,2,11,1,3,4,1).

Formula

G.f.: x*(1 - 4*x + 10*x^2 - 29*x^3 + 47*x^4 - 21*x^5 + 37*x^6 - 4*x^7 - 54*x^8 - 21*x^9 + 15*x^10 + 2*x^11 - 4*x^12 - 8*x^13 - x^14 + 2*x^15)/((1 - 2*x + x^2 - x^3 - x^4)^2*(1 - 2*x - x^2 - 2*x^4 - x^5)). - Andrew Howroyd, Dec 21 2025

Example

All solutions for n=4:
...1.0.0.1...1.1.0.1...1.0.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1
...1.0.0.1...1.0.0.1...1.0.0.1...1.0.0.1...0.0.0.1...1.0.0.1...0.0.0.1
...1.0.0.1...1.0.0.1...1.0.0.1...1.0.0.1...0.0.0.1...0.0.0.1...1.0.0.1
...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1
------
...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1...1.1.1.1
...1.0.0.0...1.0.0.0...1.0.0.1...1.0.0.1...1.0.0.1...1.0.0.1
...1.0.0.0...1.0.0.1...1.0.0.0...1.0.0.1...1.0.0.1...1.0.0.1
...1.1.1.1...1.1.1.1...1.1.1.1...1.0.0.1...1.0.1.1...1.1.0.1

Crossrefs

Row 4 of A391819.

Sequence in context: A396189 A384228 A178688 * A144472 A379290 A220249

Adjacent sequences: A163732 A163733 A163734 * A163736 A163737 A163738

Keyword

nonn,easy

Author

R. H. Hardin, Aug 03 2009

Extensions

a(22) onward from Andrew Howroyd, Dec 21 2025

Status

approved