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A252824 Number of n X 4 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

%I A252824 #6 Jun 19 2025 20:53:10
%S A252824 8,53,340,1920,9075,36292,125892,387849,1082111,2777103,6637625,
%T A252824 14922949,31813809,64737785,126429330,238046837,433778614,767506845,
%U A252824 1322268502,2223460226,3656986483,5893853502,9323072932,14495166797,22179067861
%N A252824 Number of n X 4 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.
%C A252824 Column 4 of A252828.
%H A252824 R. H. Hardin, <a href="/A252824/b252824.txt">Table of n, a(n) for n = 1..210</a>
%F A252824 Empirical: a(n) = (29/479001600)*n^12 + (29/8870400)*n^11 + (3083/43545600)*n^10 + (233/290304)*n^9 + (75539/14515200)*n^8 + (56551/2419200)*n^7 + (4051409/43545600)*n^6 + (123049/483840)*n^5 + (5473861/10886400)*n^4 + (1817149/1814400)*n^3 + (5653001/1663200)*n^2 + (23839/13860)*n + 1.
%e A252824 Some solutions for n=4
%e A252824 ..0..0..1..1....0..0..1..2....0..1..1..2....0..1..2..2....0..0..0..0
%e A252824 ..0..1..2..2....0..1..2..3....1..2..2..2....1..1..2..2....0..0..0..1
%e A252824 ..1..2..3..3....1..2..3..3....2..2..2..2....1..2..3..3....1..1..1..2
%e A252824 ..2..3..4..4....2..3..4..4....2..3..3..3....1..2..3..4....1..2..2..3
%Y A252824 Cf. A252828.
%K A252824 nonn
%O A252824 1,1
%A A252824 _R. H. Hardin_, Dec 22 2014