A323967 - OEIS

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

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OFFSET

0,3

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).

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.

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);