A323972 Number of 8 X n integer matrices (m_{i,j}) such that m_{1,1}=0, m_{8,n}=2, and all rows, columns, and falling diagonals are (weakly) monotonic without jumps of 2.

1, 21, 259, 2570, 18546, 106067, 508484, 2117690, 7852836, 26400811, 81594028, 234380304, 631352789, 1606571023, 3885713191, 8979237218, 19912769178, 42540796862, 87841523926, 175820917355, 341996038445, 647926774508, 1197980968295, 2165529201795, 3833173915877

Offset: 0

Author

Alois P. Heinz, Feb 09 2019

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Row (or column) 8 of array in A323846.

Formula

G.f.: -(6*x^17 -95*x^16 +707*x^15 -3278*x^14 +10588*x^13 -25239*x^12 +45878*x^11 -64775*x^10 +71619*x^9 -62024*x^8 +41650*x^7 -21151*x^6 +7977*x^5 -1820*x^4 +343*x^3 +38*x^2 +4*x+1) / (x-1)^17.