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A182727 Sum of largest parts of the shell model of partitions with n regions.

%I A182727 #34 Oct 15 2024 23:16:34
%S A182727 1,3,6,8,12,15,20,22,26,29,35,38,43,47,54,56,60,63,69,74,78,86,89,94,
%T A182727 98,105,108,114,119,128,130,134,137,143,148,152,160,164,171,177,182,
%U A182727 192,195,200,204,211,214,220,225,234,239,243,251,258,264,275,277,281
%N A182727 Sum of largest parts of the shell model of partitions with n regions.
%C A182727 Question: Is there some connection with fractals?
%H A182727 Alois P. Heinz, <a href="/A182727/b182727.txt">Table of n, a(n) for n = 1..4000</a>
%H A182727 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%F A182727 a(A000041(n)) = A182181(A000041(n)) = A006128(n). - _Omar E. Pol_, May 24 2012
%e A182727 For n = 6 the largest parts of the first six regions of the shell model of partitions are 1, 2, 3, 2, 4, 3, so a(6) = 1+2+3+2+4+3 = 15.
%e A182727 Written as a triangle begins:
%e A182727 1;
%e A182727 3;
%e A182727 6;
%e A182727 8,   12;
%e A182727 15,  20;
%e A182727 22,  26, 29, 35;
%e A182727 38,  43, 47, 54;
%e A182727 56,  60, 63, 69, 74, 78, 86;
%e A182727 89,  94, 98,105,108,114,119,128;
%e A182727 130,134,137,143,148,152,160,164,171,177,182,192;
%e A182727 195,200,204,211,214,220,225,234,239,243,251,258,264,275;
%Y A182727 Partial sums of A141285. Row j has length A187219(j). Right border gives A006128.
%Y A182727 Cf. A135010, A141285, A182728, A182729, A186114, A206437, A182181, A182244, A210990.
%K A182727 nonn,tabf
%O A182727 1,2
%A A182727 _Omar E. Pol_, Jan 25 2011
%E A182727 New name from _Omar E. Pol_, Apr 26 2012