A069362 Number of 4 X n binary arrays with a path of adjacent 1's from top row to bottom row.

1, 41, 1041, 22193, 433809, 8057905, 144769425, 2541013617, 43843180113, 746691527217, 12588144461329, 210502738714097, 3497001564166609, 57781030561348017, 950437243856526737, 15574913193760097649, 254416775893204873553, 4144677558181255455025

Offset: 1

Author

R. H. Hardin, Mar 22 2002

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..800
• Index entries for linear recurrences with constant coefficients, signature (35,-378,1264,-1272,-128).

Crossrefs

Row 4 of A359576.

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

Programs

Magma

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+6*x-16*x^2-8*x^3)/((1-16*x)*(1-19*x+ 74*x^2 -80*x^3-8*x^4)))); // G. C. Greubel, Apr 22 2018

Mathematica

Rest[CoefficientList[Series[x*(1+6*x-16*x^2-8*x^3)/((1-16*x)*(1-19*x+ 74*x^2 -80*x^3-8*x^4)), {x,0,50}],x]] (* G. C. Greubel, Apr 22 2018 *)
LinearRecurrence[{35,-378,1264,-1272,-128},{1,41,1041,22193,433809},20] (* Harvey P. Dale, Jan 01 2019 *)

PARI

Vec(x*(1 + 6*x - 16*x^2 - 8*x^3) / ((1 - 16*x)*(1 - 19*x + 74*x^2 - 80*x^3 - 8*x^4)) + O(x^30)) \\ Colin Barker, Oct 12 2017

Formula

G.f.: x*(1 +6*x -16*x^2 -8*x^3)/((1 -16*x)*(1 -19*x +74*x^2 -80*x^3 - 8*x^4)).