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A195524 Number of lower triangles of a 6X6 -n..n array with all row and column sums zero.

%I A195524 #7 Jul 22 2025 12:45:07
%S A195524 6247,860017,23663523,286168923,2106810049,11131321791,46387885537,
%T A195524 161770028369,491117662815,1334411256817,3311007744155,7616624997827,
%U A195524 16434220066785,33565300493927,65367853464305,122110269851089
%N A195524 Number of lower triangles of a 6X6 -n..n array with all row and column sums zero.
%C A195524 Row 6 of A195522
%H A195524 R. H. Hardin, <a href="/A195524/b195524.txt">Table of n, a(n) for n = 1..37</a>
%F A195524 Empirical: a(n) = (7389349/90720)*n^10 + (7389349/18144)*n^9 + (836251/864)*n^8 + (4318165/3024)*n^7 + (6254923/4320)*n^6 + (4563293/4320)*n^5 + (10247161/18144)*n^4 + (249983/1134)*n^3 + (21959/360)*n^2 + (3469/315)*n + 1
%e A195524 Some solutions for n=4
%e A195524 ..0............0............0............0............0............0
%e A195524 ..2-2.........-1.1.........-1.1.........-4.4..........0.0..........0.0
%e A195524 ..3-4.1.......-1.3-2.......-1-3.4........1-2.1........0-1.1.......-2.1.1
%e A195524 .-1.3-4.2.....-2.4.2-4......2-3.2-1......1.3.0-4.....-2.2.3-3.....-2.4.0-2
%e A195524 .-1.3-1-2.1....1-4.4.2-3....3.4-3-3-1...-2-1.1.3-1...-1-1.0.1.1....1-1-2.0.2
%e A195524 .-3.0.4.0-1.0..3-4-4.2.3.0.-3.1-3.4.1.0..4-4-2.1.1.0..3.0-4.2-1.0..3-4.1.2-2.0
%K A195524 nonn
%O A195524 1,1
%A A195524 _R. H. Hardin_ Sep 20 2011