%I #9 Nov 04 2024 03:22:15

%S 0,0,2,0,6,4,0,10,12,6,0,14,20,18,8,0,18,28,30,24,10,0,22,36,42,40,30,

%T 12,0,26,44,54,56,50,36,14,0,30,52,66,72,70,60,42,16,0,34,60,78,88,90,

%U 84,70,48,18,0,38,68,90,104,110,108,98,80,54,20,0,42,76,102

%N Triangle T(n,k), read by rows, given by T(n+k,k)=2*k*(2*n+1).

%C Row sums are A006331(n).

%C Diagonal sums are A212964(n+1).

%C T(2n,n)=A002943(n).

%F T(n+k,k) = A005843(k)*A005408(n).

%F Sum_{k=0..n} T(n,k) = n*(n+1)*(2*n+1)/3 = A006331(n).

%e Triangle begins:

%e 0

%e 0, 2

%e 0, 6, 4

%e 0, 10, 12, 6

%e 0, 14, 20, 18, 8

%e 0, 18, 28, 30, 24, 10

%Y Cf. columns: A000004, A016825, A017113, A017593, A051062, 10*A005408, A073762.

%Y Cf. diagonals: A005843, A008588, A008592, A008596, A008600, A008604.

%K nonn,tabl,easy,changed

%O 0,3

%A _Philippe Deléham_, Dec 05 2013