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A223868 Number of 5Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A223868 #6 Jul 23 2025 04:36:41
%S A223868 56,3136,93731,1771012,23738426,243933798,2030417942,14256118510,
%T A223868 87061570336,473468963674,2335341201122,10598137054237,44753111308505,
%U A223868 177414858857953,664941648534183,2369386354876666,8063121237072325
%N A223868 Number of 5Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A223868 Row 5 of A223864
%H A223868 R. H. Hardin, <a href="/A223868/b223868.txt">Table of n, a(n) for n = 1..210</a>
%F A223868 Empirical: a(n) = (1/7353420799762759680000000)*n^30 + (1/70032579045359616000000)*n^29 + (44267/43995432122902432972800000)*n^28 + (7069/142935127104946176000000)*n^27 + (7664593067/4032914611266056355840000000)*n^26 + (95633173/1590893337777537024000000)*n^25 + (12116718221/7445380820798873272320000)*n^24 + (43392644761/1128088003151344435200000)*n^23 + (167454195287/207507826666635264000000)*n^22 + (15612731/1026631177076736000)*n^21 + (231683957839/891769172451655680000)*n^20 + (66096734083147/16349101494947020800000)*n^19 + (200461940945639/3520141470203904000000)*n^18 + (1823522533638571/2581437078149529600000)*n^17 + (1303802945440133/173715530435474227200)*n^16 + (484634612399204963/7238147101478092800000)*n^15 + (230088704266434095413/461431877719228416000000)*n^14 + (667759304130635953/215119756512460800000)*n^13 + (1965055074194837421509/121392078599981629440000)*n^12 + (652130907487529444879/9196369590907699200000)*n^11 + (209880428234740913519/803878460743680000000)*n^10 + (4164931672385398837/5171147993088000000)*n^9 + (18238486469597047158809/8813187524619878400000)*n^8 + (16125843259442502284221/3672161468591616000000)*n^7 + (512520751978071205586267/67322960257512960000000)*n^6 + (11886431938356946376363/1122049337625216000000)*n^5 + (280599068064199101557/24311068981879680000)*n^4 + (63983220995615011/6697264182336000)*n^3 + (1678025791833176033/279770238283536000)*n^2 + (230910956201/110909026800)*n + 1
%e A223868 Some solutions for n=3
%e A223868 ..0..0..0....0..1..1....2..0..0....0..0..0....1..1..0....1..0..0....0..0..0
%e A223868 ..0..0..0....0..1..1....2..2..0....0..0..1....2..1..1....1..1..1....0..1..0
%e A223868 ..1..0..0....0..1..2....2..3..1....1..1..3....2..2..1....1..1..2....2..2..0
%e A223868 ..2..3..0....0..3..2....3..3..3....1..3..3....2..2..2....3..3..3....2..2..3
%e A223868 ..2..3..1....3..3..3....3..3..3....1..3..3....3..3..3....3..3..3....2..3..3
%K A223868 nonn
%O A223868 1,1
%A A223868 _R. H. Hardin_ Mar 28 2013