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Number of n X 4 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.
1

%I #6 Mar 15 2023 11:21:10

%S 46,698,5219,27246,115716,428949,1442005,4492529,13133871,36307595,

%T 95412314,239342404,575169570,1328404782,2957341785,6363295591,

%U 13266197675,26858140315,52913319943,101631438086,190636635796

%N Number of n X 4 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.

%C Column 4 of A224057.

%H R. H. Hardin, <a href="/A224053/b224053.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/106748928000)*n^16 + (1/2668723200)*n^15 + (29/2335132800)*n^14 + (9677/37362124800)*n^13 + (129359/28740096000)*n^12 + (171629/2874009600)*n^11 + (12139/18662400)*n^10 + (195851/37324800)*n^9 + (231935077/5225472000)*n^8 + (74110763/261273600)*n^7 + (324341569/179625600)*n^6 + (4052978161/718502400)*n^5 + (3589053277/247104000)*n^4 - (12388141/741312)*n^3 + (87129737/1029600)*n^2 + (364945/2574)*n - 457 for n>3.

%e Some solutions for n=3

%e ..0..0..0..0....0..0..0..1....0..0..0..0....0..0..1..1....2..1..0..0

%e ..2..1..1..1....0..0..1..0....2..1..0..0....0..1..2..0....1..1..1..2

%e ..1..2..2..0....1..1..1..0....1..1..2..0....1..2..1..0....1..1..2..2

%Y Cf. A224057.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 30 2013