A210953 - OEIS

A210953

Triangle read by rows: T(n,k) = sum of all parts in the k-th column of the shell model of partitions considering only the n-th shell and with its parts aligned to the right margin.

%I #15 Mar 12 2015 23:23:05

%S 1,0,3,0,0,5,0,0,2,9,0,0,0,3,12,0,0,0,2,9,20,0,0,0,0,3,11,25,0,0,0,0,

%T 2,9,22,38,0,0,0,0,0,3,14,28,49,0,0,0,0,0,2,9,26,44,69,0,0,0,0,0,0,3,

%U 14,37,55,87,0,0,0,0,0,0,2,9,29,62,83,123

%N Triangle read by rows: T(n,k) = sum of all parts in the k-th column of the shell model of partitions considering only the n-th shell and with its parts aligned to the right margin.

%e For n = 6 and k = 1..6 the 6th shell looks like this:

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

%e k: 1, 2, 3, 4, 5, 6

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

%e . 6

%e . 3 + 3

%e . 4 + 2

%e . 2 + 2 + 2

%e . 1

%e .

%e The sums of all parts in columns 1-6 are

%e . 0, 0, 0, 2, 9, 20, the same as the 6th row of triangle.

%e Triangle begins:

%e 1;

%e 0, 3;

%e 0, 0, 5;

%e 0, 0, 2, 9;

%e 0, 0, 0, 3, 12;

%e 0, 0, 0, 2, 9, 20;

%e 0, 0, 0, 0, 3, 11, 25;

%e 0, 0, 0, 0, 2, 9, 22, 38;

%e 0, 0, 0, 0, 0, 3, 14, 28, 49;

%e 0, 0, 0, 0, 0, 2, 9, 26, 44, 69;

%e 0, 0, 0, 0, 0, 0, 3, 14, 37, 55, 87;

%e 0, 0, 0, 0, 0, 0, 2, 9, 29, 62, 83, 123;

%Y Row sums give A138879. Column sums converge to A014153. Right border gives A046746, n >= 1.

%Y Cf. A135010, A138121, A210950, A210951, A210952.

%K nonn,tabl

%O 1,3

%A _Omar E. Pol_, Apr 22 2012