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A218907 Triangle, read by rows, of integer partitions of n by kernel size k.

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%I A218907 #11 Mar 12 2016 15:29:22
%S A218907 1,2,0,2,0,1,2,0,2,1,2,0,2,2,1,2,0,2,4,2,1,2,0,2,4,2,4,1,2,0,2,6,2,6,
%T A218907 2,2,2,0,2,6,2,8,2,6,2,2,0,2,8,2,8,2,12,4,2,2,0,2,8,2,10,2,14,6,8,2,2,
%U A218907 0,2,10,2,10,2,18,8,14,6,3,2,0,2,10,2,12,2,18,10,20,10,10,3,2,0,2,12,2,12,2,22,12,22,14,20,10,3,2,0,2,12,2,14,2,22,16,26,16,26,20,12,4
%N A218907 Triangle, read by rows, of integer partitions of n by kernel size k.
%C A218907 Row sum is A000041.
%C A218907 Sum k*T(n,k) = A208914(n).
%C A218907 The kernel of an integer partition is the intersection of its Ferrers diagram and of the Ferrers diagram of its conjugate.
%C A218907   Its size is between 1 (for an all-1 partition) and n (for a self-conjugate partition).
%e A218907 Triangle begins:
%e A218907 1;
%e A218907 2, 0;
%e A218907 2, 0, 1;
%e A218907 2, 0, 2,  1;
%e A218907 2, 0, 2,  2, 1;
%e A218907 2, 0, 2,  4, 2,  1;
%e A218907 2, 0, 2,  4, 2,  4, 1;
%e A218907 2, 0, 2,  6, 2,  6, 2,  2;
%e A218907 2, 0, 2,  6, 2,  8, 2,  6,  2;
%e A218907 2, 0, 2,  8, 2,  8, 2, 12,  4,  2;
%e A218907 2, 0, 2,  8, 2, 10, 2, 14,  6,  8,  2;
%e A218907 2, 0, 2, 10, 2, 10, 2, 18,  8, 14,  6,  3;
%e A218907 2, 0, 2, 10, 2, 12, 2, 18, 10, 20, 10, 10, 3;
%e A218907 2, 0, 2, 12, 2, 12, 2, 22, 12, 22, 14, 20, 10, 3;
%e A218907 2, 0, 2, 12, 2, 14, 2, 22, 16, 26, 16, 26, 20, 12, 4;
%Y A218907 Cf. A218904, A218905, A218906.
%Y A218907 Cf. A115720, A115994, A246581.
%Y A218907 Main diagonal gives A000700.
%K A218907 nonn,tabl
%O A218907 1,2
%A A218907 _Olivier Gérard_, Nov 08 2012