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A253010 Number of nX7 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down.

%I A253010 #6 Jul 23 2025 13:51:27
%S A253010 20,231,2902,33533,309990,2327062,14697256,541365583,9617848524,
%T A253010 90094114144,499454404412,1875291094664,5288570216780,12109231279152,
%U A253010 23836473347284,42007667355832,68169527721372,103870860371584
%N A253010 Number of nX7 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down.
%C A253010 Column 7 of A253011
%H A253010 R. H. Hardin, <a href="/A253010/b253010.txt">Table of n, a(n) for n = 1..210</a>
%F A253010 Empirical: a(n) = (774604193792/3)*n^3 - 8398560300416*n^2 + (277091586550828/3)*n - 343375674454152 for n>18
%e A253010 Some solutions for n=6
%e A253010 ..0..0..0..0..0..0..0....0..0..0..0..1..1..2....0..0..0..0..0..0..1
%e A253010 ..0..0..1..1..1..1..1....0..0..0..1..1..2..2....0..0..0..0..1..1..1
%e A253010 ..0..0..1..1..1..1..2....0..0..0..1..1..2..3....0..0..0..1..1..1..2
%e A253010 ..0..0..1..1..1..1..2....0..0..0..1..1..2..3....0..0..1..1..1..2..2
%e A253010 ..0..1..1..1..2..2..2....0..1..1..1..1..2..3....0..0..1..1..1..2..2
%e A253010 ..0..1..2..2..2..3..3....0..1..1..2..2..2..3....0..0..1..1..2..2..3
%K A253010 nonn
%O A253010 1,1
%A A253010 _R. H. Hardin_, Dec 25 2014