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

0,2

Links

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

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.

Crossrefs

Row (or column) 8 of array in A323846.

Sequence in context: A360804 A322500 A241632 * A125433 A135122 A231380

Adjacent sequences: A323969 A323970 A323971 * A323973 A323974 A323975

Keyword

nonn,easy

Author

Alois P. Heinz, Feb 09 2019

Status

approved