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A252825 Number of nX5 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 A252825 #6 Jul 23 2025 13:40:31
%S A252825 15,142,1238,9075,54376,271846,1165921,4396009,14863460,45791493,
%T A252825 130210765,345350438,861722537,2037396931,4591832266,9915068062,
%U A252825 20600380173,41336047432,80360448168,151781791285,279198974102
%N A252825 Number of nX5 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 A252825 Column 5 of A252828
%H A252825 R. H. Hardin, <a href="/A252825/b252825.txt">Table of n, a(n) for n = 1..210</a>
%F A252825 Empirical: a(n) = (29/130767436800)*n^15 + (29/1743565824)*n^14 + (761/1437004800)*n^13 + (4567/479001600)*n^12 + (156803/1437004800)*n^11 + (467/537600)*n^10 + (4895111/914457600)*n^9 + (8221817/304819200)*n^8 + (969313/9331200)*n^7 + (3241009/10886400)*n^6 + (129913907/179625600)*n^5 + (29795933/19958400)*n^4 + (1495061807/454053600)*n^3 + (185734933/50450400)*n^2 + (148987/27720)*n
%e A252825 Some solutions for n=4
%e A252825 ..0..1..1..2..3....0..1..1..2..2....0..1..2..3..3....0..1..2..2..2
%e A252825 ..1..2..2..3..3....0..1..1..2..3....1..2..3..3..3....1..1..2..2..3
%e A252825 ..2..2..3..3..3....1..1..1..2..3....1..2..3..4..4....1..2..3..3..4
%e A252825 ..3..3..3..4..4....1..2..2..3..4....1..2..3..4..4....2..3..4..4..5
%K A252825 nonn
%O A252825 1,1
%A A252825 _R. H. Hardin_, Dec 22 2014