A069325 Number of 3 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

1, 8, 51, 295, 1632, 8830, 47239, 251261, 1332456, 7055228, 37327007, 197404203, 1043751584, 5518106750, 29171471659, 154210451661, 815197197636, 4309313949364, 22779900825195, 120418887728947

Offset: 1

Author

R. H. Hardin, Mar 16 2002

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1383
• Index entries for linear recurrences with constant coefficients, signature (9,-21,3,24,-8,-4,4).

Crossrefs

Row 3 of A359575.

Cf. 2 X n A048739, 4 X n A069326, 5 X n A069327, 6 X n A069328, 7 X n A069329, 8 X n A069330, 9 X n A069331, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.

Programs

Magma

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1-x+x^3)/((1-2*x-2*x^2)*(2*x^5-4*x^4+x^3+9*x^2-7*x+1)))); // G. C. Greubel, Apr 22 2018

Mathematica

CoefficientList[Series[x*(1-x+x^3)/((1-2*x-2*x^2)*(2*x^5-4*x^4+x^3+9*x^2 -7*x+1)), {x, 0, 50}], x] (* G. C. Greubel, Apr 22 2018 *)
LinearRecurrence[{9,-21,3,24,-8,-4,4},{1,8,51,295,1632,8830,47239},20] (* Harvey P. Dale, May 21 2023 *)

PARI

Vec(-x*(1-x+x^3)/(2*x^2+2*x-1)/(2*x^5-4*x^4+x^3+9*x^2-7*x+1) + O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

Formula

G.f.: x*(1-x+x^3)/((1-2*x-2*x^2)*(2*x^5-4*x^4+x^3+9*x^2-7*x+1)). - Vladeta Jovovic, Jul 02 2003