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.

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

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

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

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

Adjacent sequences: A323965 A323966 A323967 * A323969 A323970 A323971

Keyword

nonn,easy

Author

Alois P. Heinz, Feb 09 2019

Status

approved