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A214012 Number of 3X3 nonnegative integer matrices with row and column i=1..3 having sum <= i*n.

%I A214012 #10 Jul 22 2025 23:06:44
%S A214012 271,7722,85639,564041,2663506,9976732,31499434,87205393,217519577,
%T A214012 498458246,1064675833,2143185161,4101100212,7511389208,13241320196,
%U A214012 22569031649,37334466803,60131772546,94551181659,145479371081
%N A214012 Number of 3X3 nonnegative integer matrices with row and column i=1..3 having sum <= i*n.
%C A214012 Row 3 of A214011
%H A214012 R. H. Hardin, <a href="/A214012/b214012.txt">Table of n, a(n) for n = 1..210</a>
%F A214012 Empirical: a(n) = (n+3) *(n+2) *(n+1) *(3493*n^6 +23853*n^5 +62185*n^4 +81783*n^3 +58531*n^2 +22470*n +3780)/22680;
%e A214012 Some solutions for n=3
%e A214012 ..0..0..1....0..0..2....3..0..0....0..0..3....0..0..3....0..0..0....2..0..0
%e A214012 ..2..0..0....2..1..0....0..6..0....1..2..0....1..0..0....0..0..0....0..1..0
%e A214012 ..0..6..0....0..0..5....0..0..9....2..1..0....0..3..4....0..4..0....1..2..0
%K A214012 nonn
%O A214012 1,1
%A A214012 _R. H. Hardin_ Jun 30 2012