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A223867 Number of 4Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A223867 #6 Jul 23 2025 04:36:35
%S A223867 35,1225,24199,315124,3017129,22852913,144081276,784071455,3781718633,
%T A223867 16487698435,65952999251,244841613810,851144356707,2790551617469,
%U A223867 8678912669190,25728520577688,72995578880032,198891717017532
%N A223867 Number of 4Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A223867 Row 4 of A223864
%H A223867 R. H. Hardin, <a href="/A223867/b223867.txt">Table of n, a(n) for n = 1..210</a>
%F A223867 Empirical: a(n) = (1/2906843957821440000)*n^24 + (1/34605285212160000)*n^23 + (2197/1372406261022720000)*n^22 + (37133/608225502044160000)*n^21 + (45197/25276903981056000)*n^20 + (14623277/347557429739520000)*n^19 + (26489599/32011868528640000)*n^18 + (37041601/2667655710720000)*n^17 + (14981899/74392141824000)*n^16 + (19115865583/7532204359680000)*n^15 + (31834111187/1158800670720000)*n^14 + (66986419663/269007298560000)*n^13 + (122476645127999/66283398365184000)*n^12 + (27904576042121/2510734786560000)*n^11 + (949107163427/17557585920000)*n^10 + (100270802691019/470762772480000)*n^9 + (174267558093661/256094948229120)*n^8 + (2011492987640933/1143281018880000)*n^7 + (61760354830949111/16895152834560000)*n^6 + (4216963085471057/703964701440000)*n^5 + (5310598072571189/703964701440000)*n^4 + (2777655817513/391091500800)*n^3 + (19272574007557/3805621142400)*n^2 + (2059892117/1070845776)*n + 1
%e A223867 Some solutions for n=3
%e A223867 ..2..1..1....3..3..0....0..0..2....0..2..1....0..2..0....1..1..0....0..0..0
%e A223867 ..2..3..1....3..3..1....0..3..2....2..3..1....1..2..0....2..1..0....0..1..0
%e A223867 ..2..3..1....3..3..1....0..3..2....2..3..1....2..3..0....2..2..1....0..3..3
%e A223867 ..2..3..2....3..3..3....1..3..3....3..3..3....3..3..3....2..3..2....0..3..3
%K A223867 nonn
%O A223867 1,1
%A A223867 _R. H. Hardin_ Mar 28 2013