A138978 Number of 3 X n matrices containing a 1 in the top left entry, all entries are integer values and adjacent entries differ by at most 1.

9, 121, 1665, 22979, 317259, 4380445, 60481881, 835088891, 11530288395, 159201677509, 2198138788809, 30350271502115, 419054058355851, 5785987905016141, 79888633386248025, 1103043049708026539, 15230001039404897259, 210284568423392013685, 2903453493049800669321

Offset

1,1

Comments

Horizontally or vertically adjacent entries can differ by at most 1. Diagonally adjacent entries thus differ by at most 2.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..800

Index entries for linear recurrences with constant coefficients, signature (16,-31,10).

Formula

a(n) = b(n)+c(n)+d(n), where b(1)=1, c(1)=6, d(1)=2, with b(n+1)=3*b(n)+2*c(n)+1*d(n), c(n+1)=12*b(n)+10*c(n)+6*d(n), d(n+1)=2*b(n)+2*c(n)+3*d(n).

G.f.: -x*(8*x^2-23*x+9) / (10*x^3-31*x^2+16*x-1). - Colin Barker, Dec 03 2012

Maple

a:= n-> (Matrix([1, 6, 2]). Matrix([[3, 12, 2], [2, 10, 2], [1, 6, 3]])^(n-1) .Matrix([[1], [1], [1]]))[1, 1]: seq(a(n), n=1..20); # Alois P. Heinz, Aug 28 2008]

Mathematica

LinearRecurrence[{16, -31, 10}, {9, 121, 1665}, 25] (* Paolo Xausa, Mar 17 2024 *)

Crossrefs

Cf. A138977, A138979.

Sequence in context: A103930 A302941 A183514 * A046184 A084769 A246467

Adjacent sequences: A138975 A138976 A138977 * A138979 A138980 A138981

Keyword

nonn,easy

Author

Wayne VanWeerthuizen, Apr 05 2008

Extensions

More terms from Alois P. Heinz, Aug 28 2008

Status

approved