login
A323968
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.
2
1, 3, 16, 94, 386, 1247, 3423, 8342, 18546, 38304, 74451, 137503, 243103, 413858, 681632, 1090365, 1699493, 2588049, 3859530, 5647620, 8122864, 11500393, 16048805, 22100312, 30062268, 40430198, 53802453, 70896621, 92567829, 119829076, 153873742, 196100423
OFFSET
0,2
LINKS
FORMULA
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.
MAPLE
a:= n-> `if`(n=0, 1, 3+((((((((5*n+100)*n+826)*n+4984)*n+15925)*n
+20020)*n-16756)*n-25104)*n)/40320):
seq(a(n), n=0..35);
CROSSREFS
Row (or column) 4 of array in A323846.
Sequence in context: A221764 A371742 A213229 * A074555 A137644 A114174
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Feb 09 2019
STATUS
approved