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.

1, 1, 4, 25, 94, 266, 632, 1332, 2570, 4631, 7900, 12883, 20230, 30760, 45488, 65654, 92754, 128573, 175220, 235165, 311278, 406870, 525736, 672200, 851162, 1068147, 1329356, 1641719, 2012950, 2451604, 2967136, 3569962, 4271522, 5084345, 6022116, 7099745

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
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Row (or column) 3 of array in A323846.

Programs

Maple

a:= n-> `if`(n=0, 1, 2+((((((n+12)*n+55)*n+120)*n-236)*n-312)*n)/360):
seq(a(n), n=0..40);

Formula

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.

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