A163049 Number of n X 5 binary arrays with all 1s connected, and all corners 1.

1, 17, 293, 5331, 101950, 1988608, 39005563, 765978583, 15044778941, 295502003013, 5804078824664, 114000099400204, 2239117437370843, 43979313642748723, 863813545775995327, 16966473035357220851, 333244608914862669888, 6545377413296547714370, 128560115721002848505333

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (39,-547,4079,-17927,44032, -29646,-161261,507392,-444090, -488756,980592,-101650,1438895, -4174679,-1246016,8663468,-3414959, 510459,-1716806,-2980202,5525320, 331308,-2267390,612301,136350, -115804,34459,-4461,-99,49,-1).

Formula

G.f.: x*(1 - 22*x + 177*x^2 - 876*x^3 + 2896*x^4 - 5805*x^5 + 5065*x^6 + 8856*x^7 - 31486*x^8 + 41679*x^9 - 47207*x^10 + 65101*x^11 - 25411*x^12 - 37423*x^13 - 4518*x^14 - 194303*x^15 + 162017*x^16 - 50829*x^17 + 94223*x^18 + 130631*x^19 - 174278*x^20 - 22494*x^21 + 47475*x^22 + 3545*x^23 - 6614*x^24 + 62*x^25 + 329*x^26 - 22*x^27 - x^28)/(1 - 39*x + 547*x^2 - 4079*x^3 + 17927*x^4 - 44032*x^5 + 29646*x^6 + 161261*x^7 - 507392*x^8 + 444090*x^9 + 488756*x^10 - 980592*x^11 + 101650*x^12 - 1438895*x^13 + 4174679*x^14 + 1246016*x^15 - 8663468*x^16 + 3414959*x^17 - 510459*x^18 + 1716806*x^19 + 2980202*x^20 - 5525320*x^21 - 331308*x^22 + 2267390*x^23 - 612301*x^24 - 136350*x^25 + 115804*x^26 - 34459*x^27 + 4461*x^28 + 99*x^29 - 49*x^30 + x^31). - Andrew Howroyd, Oct 26 2025

Crossrefs

Column 5 of A389687.

Sequence in context: A041546 A186000 A222572 * A083453 A090437 A007805

Adjacent sequences: A163046 A163047 A163048 * A163050 A163051 A163052

Keyword

nonn,easy

Author

R. H. Hardin, Jul 20 2009

Extensions

a(17) onward from Andrew Howroyd, Oct 26 2025

Status

approved