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%I #6 Jun 26 2022 03:29:20
%S 42,729,10761,125892,1165921,8807722,55960651,306796310,1481748658,
%T 6411737114,25203579317,91037124979,305083525901,956286103952,
%U 2823092600299,7895877354183,21029532417878,53571661955209
%N Number of n X 7 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 Column 7 of A252828.
%H R. H. Hardin, <a href="/A252827/b252827.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (491/510909421717094400)*n^21 + (491/4054836680294400)*n^20 + (31237/4561691265331200)*n^19 + (16931/72754246656000)*n^18 + (6860417/1280474741145600)*n^17 + (5620079/62768369664000)*n^16 + (28238557/24715045555200)*n^15 + (460207/39626496000)*n^14 + (1996189759/20542375526400)*n^13 + (9849852413/14485008384000)*n^12 + (262128023/65840947200)*n^11 + (23507656471/1207084032000)*n^10 + (126607207245823/1581762915532800)*n^9 + (1573022155907/5706215424000)*n^8 + (887749472755/1129830653952)*n^7 + (43972723546711/23538138624000)*n^6 + (101853364790929/26676557107200)*n^5 + (13152985155929/2020951296000)*n^4 + (11601438763393/1119943843200)*n^3 + (5765297083043/586637251200)*n^2 + (131188073/15519504)*n.
%e Some solutions for n=4
%e ..0..1..2..2..3..4..4....0..1..2..3..3..4..5....0..1..2..3..3..4..5
%e ..1..2..3..3..4..5..5....0..1..2..3..4..5..5....1..2..3..3..4..5..5
%e ..1..2..3..4..4..5..5....1..1..2..3..4..5..5....1..2..3..4..5..5..6
%e ..2..3..4..5..5..6..6....1..2..3..3..4..5..6....2..3..4..4..5..5..6
%Y Cf. A252828.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 22 2014
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