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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.
5
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.
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
Sequence in context: A103930 A302941 A183514 * A046184 A084769 A246467
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Alois P. Heinz, Aug 28 2008
STATUS
approved