login
Triangle read by rows: T(n,k) (n>=k>=1) = ceiling((n/k)*ceiling(n/k)).
9

%I #10 Dec 02 2020 05:34:29

%S 1,4,1,9,3,1,16,4,3,1,25,8,4,3,1,36,9,4,3,3,1,49,14,7,4,3,3,1,64,16,8,

%T 4,4,3,3,1,81,23,9,7,4,3,3,3,1,100,25,14,8,4,4,3,3,3,1,121,33,15,9,7,

%U 4,4,3,3,3,1,144,36,16,9,8,4,4,3,3,3,3,1,169,46,22,13,8,7,4,4,3,3,3,3,1

%N Triangle read by rows: T(n,k) (n>=k>=1) = ceiling((n/k)*ceiling(n/k)).

%H Robert J. McEliece and Herbert Taylor, <a href="https://doi.org/10.1016/0097-3165(73)90069-1">Covering tori with squares</a>, Journal of Combinatorial Theory, Series A 14.1 (1973): 119-124.

%e Triangle begins:

%e 1,

%e 4, 1,

%e 9, 3, 1,

%e 16, 4, 3, 1,

%e 25, 8, 4, 3, 1,

%e 36, 9, 4, 3, 3, 1,

%e 49, 14, 7, 4, 3, 3, 1,

%e 64, 16, 8, 4, 4, 3, 3, 1,

%e 81, 23, 9, 7, 4, 3, 3, 3, 1,

%e 100, 25, 14, 8, 4, 4, 3, 3, 3, 1,

%e 121, 33, 15, 9, 7, 4, 4, 3, 3, 3, 1,

%e 144, 36, 16, 9, 8, 4, 4, 3, 3, 3, 3, 1,

%e 169, 46, 22, 13, 8, 7, 4, 4, 3, 3, 3, 3, 1,

%e ...

%Y Cf. A331146-A331154.

%K nonn,tabl

%O 1,2

%A _N. J. A. Sloane_, Jan 14 2020