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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 19 14:36 EDT 2019. Contains 323395 sequences. (Running on oeis4.)