A195892 - OEIS

%I #8 May 11 2022 03:27:17

%S 1,1,1,1,1,3,1,1,5,15,1,1,7,65,83,1,1,9,175,1349,591,1,1,11,369,14831,

%T 90013,5281,1,1,13,671,68551,4857647,17612909,56249,1,1,15,1105,

%U 241221,65530899,5181491667,7690681987,704129,1,1,17,1695,680115,584257875

%N T(n,k) = Number of lower triangles of an n X n integer array with all row and column sums zero and all row and column sums of squares <= 2k^2.

%C Table starts

%C ......1..........1..........1............1.........1......1....1..1.1.1

%C ......1..........1..........1............1.........1......1....1..1.1

%C ......3..........5..........7............9........11.....13...15.17

%C .....15.........65........175..........369.......671...1105.1695

%C .....83.......1349......14831........68551....241221.680115

%C ....591......90013....4857647.....65530899.584257875

%C ...5281...17612909.5181491667.314737269521

%C ..56249.7690681987

%C .704129

%H R. H. Hardin, <a href="/A195892/b195892.txt">Table of n, a(n) for n = 1..52</a>

%e Some solutions for n=5 k=4

%e ..0..........0..........0..........0..........0..........0..........0

%e .-1.1........1-1.......-4.4........3-3........1-1........2-2........3-3

%e .-2.1.1.....-2.4-2......3-3.0......0.3-3.....-2.4-2.....-4.3.1......0-1.1

%e ..0-1-1.2...-2-1.2.1....1-1-3.3...-1-1.0.2....0-2-1.3....1-2.0.1....1.0-1.0

%e ..3-1.0-2.0..3-2.0-1.0..0.0.3-3.0.-2.1.3-2.0..1-1.3-3.0..1.1-1-1.0.-4.4.0.0.0

%K nonn,tabl

%O 1,6

%A _R. H. Hardin_, Sep 24 2011