A163013 Number of n X 4 binary arrays with all 1s connected and a path of 1s from top row to lower right corner.

4, 44, 469, 4776, 48047, 482895, 4854639, 48809845, 490753552, 4934223120, 49610514652, 498802509247, 5015145456885, 50424133267633, 506982946384063, 5097394665460444, 51251097416909895, 515297550767237152, 5180992782786954916, 52091623908067478071, 523748515997835053976

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500 (terms 1..44 from R. H. Hardin)

Index entries for linear recurrences with constant coefficients, signature (15,-59,97,-19,-210,222,22,-113,7,-71,13,1).

Formula

Empirical: a(n)= 15*a(n-1) -59*a(n-2) +97*a(n-3) -19*a(n-4) -210*a(n-5) +222*a(n-6) +22*a(n-7) -113*a(n-8) +7*a(n-9) -71*a(n-10) +13*a(n-11) +a(n-12). - R. J. Mathar, Aug 11 2009

Formula confirmed using the transfer matrix method. - Andrew Howroyd, Dec 24 2025

G.f.: x*(4 - 16*x + 45*x^2 - 51*x^3 - 114*x^4 + 157*x^5 - 22*x^6 - 116*x^7 - 18*x^8 - 59*x^9 + 13*x^10 + x^11)/(1 - 15*x + 59*x^2 - 97*x^3 + 19*x^4 + 210*x^5 - 222*x^6 - 22*x^7 + 113*x^8 - 7*x^9 + 71*x^10 - 13*x^11 - x^12). - Andrew Howroyd, Dec 24 2025

Crossrefs

Column 4 of A391489.

Sequence in context: A105038 A002278 A112897 * A087813 A342346 A082779

Adjacent sequences: A163010 A163011 A163012 * A163014 A163015 A163016

Keyword

nonn,easy

Author

R. H. Hardin, Jul 20 2009

Status

approved