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A323967 Number of 3 X n integer matrices (m_{i,j}) such that m_{1,1}=0, m_{3,n}=2, and all rows, columns, and falling diagonals are (weakly) monotonic without jumps of 2. 2

%I

%S 1,1,4,25,94,266,632,1332,2570,4631,7900,12883,20230,30760,45488,

%T 65654,92754,128573,175220,235165,311278,406870,525736,672200,851162,

%U 1068147,1329356,1641719,2012950,2451604,2967136,3569962,4271522,5084345,6022116,7099745

%N Number of 3 X n integer matrices (m_{i,j}) such that m_{1,1}=0, m_{3,n}=2, and all rows, columns, and falling diagonals are (weakly) monotonic without jumps of 2.

%H Alois P. Heinz, <a href="/A323967/b323967.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F G.f.: -(x^7-5*x^6+7*x^5+3*x^4-17*x^3+18*x^2-6*x+1)/(x-1)^7.

%F a(n) = 2+((((((n+12)*n+55)*n+120)*n-236)*n-312)*n)/360 for n > 0, a(0) = 1.

%p a:= n-> `if`(n=0, 1, 2+((((((n+12)*n+55)*n+120)*n-236)*n-312)*n)/360):

%p seq(a(n), n=0..40);

%Y Row (or column) 3 of array in A323846.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Feb 09 2019

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Last modified June 25 10:48 EDT 2019. Contains 324351 sequences. (Running on oeis4.)