A232614 - OEIS

A232614

T(n,k) is the number of (n+1) X (k+1) 0..2 arrays x(i,j) with every row Sum_{j=1..k+1} j*x(i,j) equal, and every column Sum_{i=1..n+1} i*x(i,j) equal.

%I #8 Feb 08 2025 09:01:21

%S 5,5,5,3,13,3,9,13,13,9,11,23,61,23,11,3,45,93,93,45,3,23,105,105,713,

%T 105,105,23,37,297,493,1521,1521,493,297,37,3,583,1927,6561,40917,

%U 6561,1927,583,3,95,1419,16121,53539,193015,193015,53539,16121,1419,95,159

%N T(n,k) is the number of (n+1) X (k+1) 0..2 arrays x(i,j) with every row Sum_{j=1..k+1} j*x(i,j) equal, and every column Sum_{i=1..n+1} i*x(i,j) equal.

%H R. H. Hardin, <a href="/A232614/b232614.txt">Table of n, a(n) for n = 1..83</a>

%e Table starts:

%e ..5....5......3.......9.......11........3.......23.......37.........3.......95

%e ..5...13.....13......23.......45......105......297......583......1419.....4299

%e ..3...13.....61......93......105......493.....1927....16121.....63829...119777

%e ..9...23.....93.....713.....1521.....6561....53539...912585...2788563.18652349

%e .11...45....105....1521....40917...193015..1135417.14754807.209747055

%e ..3..105....493....6561...193015.10996137.58912359

%e .23..297...1927...53539..1135417.58912359

%e .37..583..16121..912585.14754807

%e ..3.1419..63829.2788563

%e .95.4299.119777

%e Some solutions for n=3 and k=4:

%e ..2..0..1..0..2....0..1..2..1..0....0..2..1..2..0....0..0..0..0..0

%e ..0..2..1..2..0....0..2..0..2..0....2..0..1..0..2....0..0..0..0..0

%e ..0..2..1..2..0....0..1..2..1..0....2..0..1..0..2....0..0..0..0..0

%e ..2..0..1..0..2....2..0..0..0..2....0..2..1..2..0....0..0..0..0..0

%K nonn,tabl,changed

%O 1,1

%A _R. H. Hardin_, Nov 26 2013