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

1,2

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).

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)).

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 *)

Prog

(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
(Magma) m:=25; R<x>:=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

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.

Sequence in context: A091314 A059762 A368809 * A016093 A358713 A130639

Adjacent sequences: A069359 A069360 A069361 * A069363 A069364 A069365

Keyword

nonn,easy

Author

R. H. Hardin, Mar 22 2002

Status

approved