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%I #7 Feb 09 2019 19:40:04
%S 1,3,16,94,386,1247,3423,8342,18546,38304,74451,137503,243103,413858,
%T 681632,1090365,1699493,2588049,3859530,5647620,8122864,11500393,
%U 16048805,22100312,30062268,40430198,53802453,70896621,92567829,119829076,153873742,196100423
%N Number of 4 X n integer matrices (m_{i,j}) such that m_{1,1}=0, m_{4,n}=2, and all rows, columns, and falling diagonals are (weakly) monotonic without jumps of 2.
%H Alois P. Heinz, <a href="/A323968/b323968.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F G.f.: -(2*x^9-15*x^8+47*x^7-78*x^6+65*x^5-10*x^4-26*x^3+25*x^2-6*x+1)/(x-1)^9.
%p a:= n-> `if`(n=0, 1, 3+((((((((5*n+100)*n+826)*n+4984)*n+15925)*n
%p +20020)*n-16756)*n-25104)*n)/40320):
%p seq(a(n), n=0..35);
%Y Row (or column) 4 of array in A323846.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Feb 09 2019
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