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A252819 Number of nX7 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

%I A252819 #6 Jul 23 2025 13:40:11
%S A252819 22,246,2067,13015,65711,279300,1033761,3414257,10248688,28359679,
%T A252819 73160199,177550620,408377425,895696589,1883020893,3810974274,
%U A252819 7452779978,14128342036,26035049083,46748705613,81968236755,140604294490
%N A252819 Number of nX7 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.
%C A252819 Column 7 of A252820
%H A252819 R. H. Hardin, <a href="/A252819/b252819.txt">Table of n, a(n) for n = 1..210</a>
%F A252819 Empirical: a(n) = (1/660441600)*n^14 + (1/9434880)*n^13 + (1/311850)*n^12 + (283/4989600)*n^11 + (23/34560)*n^10 + (5/896)*n^9 + (55843/1587600)*n^8 + (153973/907200)*n^7 + (4462807/7257600)*n^6 + (239717/145152)*n^5 + (50459/14400)*n^4 + (1240207/302400)*n^3 + (269664683/50450400)*n^2 + (308941/120120)*n + 4
%e A252819 Some solutions for n=4
%e A252819 ..0..1..1..2..3..4..5....0..1..2..3..4..5..5....0..1..2..3..3..4..4
%e A252819 ..0..1..2..3..3..4..5....1..2..3..3..4..5..5....1..2..3..3..4..4..5
%e A252819 ..1..2..3..3..4..5..6....2..3..3..4..5..6..6....1..2..3..4..5..5..6
%e A252819 ..2..3..4..4..5..6..7....3..4..4..5..6..7..7....1..2..3..4..5..6..7
%K A252819 nonn
%O A252819 1,1
%A A252819 _R. H. Hardin_, Dec 22 2014