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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 (list; graph; refs; listen; history; text; internal format)
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: A305852 A221764 A213229 * A074555 A137644 A114174

Adjacent sequences:  A323965 A323966 A323967 * A323969 A323970 A323971

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Feb 09 2019

STATUS

approved

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Last modified October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)