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A210966 Sum of all region numbers of all parts of the n-th region of the shell model of partitions.

%I A210966 #13 Mar 11 2014 01:34:20
%S A210966 1,4,9,4,25,6,49,8,18,10,121,12,26,14,225,16,34,18,76,20,21,484,23,48,
%T A210966 25,104,27,56,29,900,31,64,33,136,35,36,259,38,78,40,41,1764,43,88,45,
%U A210966 184,47,96,49,400,51,52,159,54,55,3136,57,116,59,240
%N A210966 Sum of all region numbers of all parts of the n-th region of the shell model of partitions.
%C A210966 Each part of a partition of n belongs to a different region of n. The "region number" of a part of the r-th region of n is equal to r. For the definition of "region of n" see A206437.
%H A210966 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%F A210966 a(n) = n*A194446(n).
%e A210966 The first seven regions of the shell model of partitions (or the seven regions of 5) are [1], [2, 1], [3, 1, 1], [2], [4, 2, 1, 1, 1], [3], [5, 2, 1, 1, 1, 1, 1] therefore the "region numbers" are [1], [2, 2], [3, 3, 3], [4], [5, 5, 5, 5, 5], [6], [7, 7, 7, 7, 7, 7, 7]. So a(1)..a(7) give: 1, 4, 9, 4, 25, 6, 49.
%e A210966 Also written as an irregular triangle the sequence begins:
%e A210966 1;
%e A210966 4;
%e A210966 9;
%e A210966 4,25;
%e A210966 6,49;
%e A210966 8,18,10,121;
%e A210966 12,26,14,225;
%e A210966 16,34,18,76,20,21,484;
%e A210966 23,48,25,104,27,56,29,900;
%e A210966 31,64,33,136,35,36,259,38,78,40,41,1764;
%e A210966 43,88,45,184,47,96,49,400,51,52,159,54,55,3136;
%Y A210966 Row n has length A187219(n). Row sums give A210969. Right border gives A001255, n >= 1.
%Y A210966 Cf. A135010, A138121, A194446, A182703, A206437, A210971, A210972.
%K A210966 nonn,tabf
%O A210966 1,2
%A A210966 _Omar E. Pol_, Jul 01 2012