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

0,3

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);

Crossrefs

Row (or column) 3 of array in A323846.

Sequence in context: A041991 A027764 A095669 * A195509 A027949 A226547

Adjacent sequences: A323964 A323965 A323966 * A323968 A323969 A323970

Keyword

nonn,easy

Author

Alois P. Heinz, Feb 09 2019

Status

approved