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A223967 Number of 7Xn 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A223967 #6 Jul 23 2025 04:43:16
%S A223967 16384,3342081,68892600,559416917,2772658693,10269723035,31770135236,
%T A223967 87719331172,225263690895,552379261275,1315281342539,3072993757981,
%U A223967 7087865594659,16189704679316,36662195998974,82296709582927
%N A223967 Number of 7Xn 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A223967 Row 7 of A223961
%H A223967 R. H. Hardin, <a href="/A223967/b223967.txt">Table of n, a(n) for n = 1..210</a>
%F A223967 Empirical: a(n) = (1/36870930432000)*n^21 + (1/1755758592000)*n^20 + (7987/292065067008000)*n^19 + (193003/284549942476800)*n^18 + (17759011/1067062284288000)*n^17 + (1347607/3804143616000)*n^16 + (18694718671/2636271525888000)*n^15 + (3112211369/25107347865600)*n^14 + (20604917909/9782083584000)*n^13 + (70370427983/2145927168000)*n^12 + (1850924201039/3862668902400)*n^11 + (147887455837/23410114560)*n^10 + (3273669680467127/40558023475200)*n^9 + (412868001184691/482833612800)*n^8 + (28540139678997911/3362591232000)*n^7 + (7031336918804501/95103590400)*n^6 + (100407456813399821/290594304000)*n^5 + (203722361032935541/108972864000)*n^4 - (63818340288729017/11557728000)*n^3 - (185169857197901243/1286485200)*n^2 + (456453009190537/5819814)*n + 2553072919 for n>14
%e A223967 Some solutions for n=3
%e A223967 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A223967 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A223967 ..0..0..0....0..0..0....0..0..1....0..0..0....0..0..3....0..0..1....0..0..0
%e A223967 ..0..0..0....0..0..3....0..2..3....0..0..0....0..1..2....0..0..3....0..0..2
%e A223967 ..0..0..0....0..1..1....0..1..3....1..1..3....0..3..3....0..1..1....1..1..1
%e A223967 ..0..0..2....1..1..3....0..3..3....0..2..2....1..1..3....1..1..2....1..1..1
%e A223967 ..0..1..1....0..1..2....0..2..3....1..2..3....1..1..1....1..2..2....2..3..3
%K A223967 nonn
%O A223967 1,1
%A A223967 _R. H. Hardin_ Mar 29 2013