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%I #22 Mar 17 2024 15:35:14
%S 9,121,1665,22979,317259,4380445,60481881,835088891,11530288395,
%T 159201677509,2198138788809,30350271502115,419054058355851,
%U 5785987905016141,79888633386248025,1103043049708026539,15230001039404897259,210284568423392013685,2903453493049800669321
%N 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.
%C Horizontally or vertically adjacent entries can differ by at most 1. Diagonally adjacent entries thus differ by at most 2.
%H Alois P. Heinz, <a href="/A138978/b138978.txt">Table of n, a(n) for n = 1..800</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (16,-31,10).
%F 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).
%F G.f.: -x*(8*x^2-23*x+9) / (10*x^3-31*x^2+16*x-1). - _Colin Barker_, Dec 03 2012
%p 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]
%t LinearRecurrence[{16, -31, 10}, {9, 121, 1665}, 25] (* _Paolo Xausa_, Mar 17 2024 *)
%Y Cf. A138977, A138979.
%K nonn,easy
%O 1,1
%A _Wayne VanWeerthuizen_, Apr 05 2008
%E More terms from _Alois P. Heinz_, Aug 28 2008
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