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Triangle read by rows: T(n,k) = A024916(k)*A002865(n-k).
7

%I #17 Jul 17 2014 19:55:44

%S 1,0,4,1,0,8,1,4,0,15,2,4,8,0,21,2,8,8,15,0,33,4,8,16,15,21,0,41,4,16,

%T 16,30,21,33,0,56,7,16,32,30,42,33,41,0,69,8,28,32,60,42,66,41,56,0,

%U 87,12,32,56,60,84,66,82,56,69,0,99,14,48,64

%N Triangle read by rows: T(n,k) = A024916(k)*A002865(n-k).

%C Row sums give A066186.

%C Column 1 is A002865.

%C Leading diagonal is A024916.

%C Since A024916(k) has a symmetric representation then both T(n,k) and the partial sums of row n can be represented by symmetric polycubes - for more information see A237593 and A237270. For another version see A221529.

%e Triangle begins:

%e 1;

%e 0, 4;

%e 1, 0, 8;

%e 1, 4, 0, 15;

%e 2, 4, 8, 0, 21;

%e 2, 8, 8, 15, 0, 33;

%e 4, 8, 16, 15, 21, 0, 41;

%e 4, 16, 16, 30, 21, 33, 0, 56;

%e 7, 16, 32, 30, 42, 33, 41, 0, 69;

%e 8, 28, 32, 60, 42, 66, 41, 56, 0, 87;

%e 12, 32, 56, 60, 84, 66, 82, 56, 69, 0, 99;

%e ...

%e For n = 6:

%e -------------------------

%e k A024916 T(6,k)

%e -------------------------

%e 1 1 * 2 = 2

%e 2 4 * 2 = 8

%e 3 8 * 1 = 8

%e 4 15 * 1 = 15

%e 5 21 * 0 = 0

%e 6 33 * 1 = 33

%e . A002865

%e -------------------------

%e So row 6 is [2, 8, 8, 15, 0, 33] and the sum of row 6 is 2+8+8+15+0+33 = 66 equaling A066186(6) = 6*A000041(6) = 6*11 = 66.

%Y Cf. A000041, A000203, A002865, A024916, A066186, A221529, A221530, A245095.

%K nonn,tabl

%O 1,3

%A _Omar E. Pol_, Jul 13 2014