A182727 - OEIS

%I #34 Oct 15 2024 23:16:34

%S 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 98,105,108,114,119,128,130,134,137,143,148,152,160,164,171,177,182,

%U 192,195,200,204,211,214,220,225,234,239,243,251,258,264,275,277,281

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

%C Question: Is there some connection with fractals?

%H Alois P. Heinz, <a href="/A182727/b182727.txt">Table of n, a(n) for n = 1..4000</a>

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>

%F a(A000041(n)) = A182181(A000041(n)) = A006128(n). - _Omar E. Pol_, May 24 2012

%e 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 Written as a triangle begins:

%e 1;

%e 3;

%e 6;

%e 8,   12;

%e 15,  20;

%e 22,  26, 29, 35;

%e 38,  43, 47, 54;

%e 56,  60, 63, 69, 74, 78, 86;

%e 89,  94, 98,105,108,114,119,128;

%e 130,134,137,143,148,152,160,164,171,177,182,192;

%e 195,200,204,211,214,220,225,234,239,243,251,258,264,275;

%Y Partial sums of A141285. Row j has length A187219(j). Right border gives A006128.

%Y Cf. A135010, A141285, A182728, A182729, A186114, A206437, A182181, A182244, A210990.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Jan 25 2011

%E New name from _Omar E. Pol_, Apr 26 2012