cp's OEIS Frontend

A182244 Sum of all parts of the shell model of partitions of A135010 with n regions.

%I A182244 #27 Jul 25 2020 12:16:15
%S A182244 1,4,9,11,20,23,35,37,43,46,66,69,76,80,105,107,113,116,129,134,138,
%T A182244 176,179,186,190,204,207,216,221,270,272,278,281,294,299,303,326,330,
%U A182244 340,346,351,420,423,430,434,448,451,460,465,492,497,501,516,523,529,616
%N A182244 Sum of all parts of the shell model of partitions of A135010 with n regions.
%H A182244 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%F A182244 a(A000041(k)) = A066186(k), k >= 1.
%e A182244 The first four regions of the shell model of partitions are [1],[2, 1],[3, 1, 1],[2], so a(4) = (1)+(2+1)+(3+1+1)+(2) = 11.
%e A182244 Written as a triangle begins:
%e A182244 1;
%e A182244 4;
%e A182244 9;
%e A182244 11,  20;
%e A182244 23,  35;
%e A182244 37,  43, 46, 66;
%e A182244 69,  76, 80,105;
%e A182244 107,113,116,129,134,138,176;
%e A182244 179,186,190,204,207,216,221,270;
%e A182244 272,278,281,294,299,303,326,330,340,346,351,420;
%e A182244 423,430,434,448,451,460,465,492,497,501,516,523,529,616;
%e A182244 ...
%e A182244 From _Omar E. Pol_, Aug 08 2013: (Start)
%e A182244 Illustration of initial terms:
%e A182244 .                                                _ _ _ _ _
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%e A182244 .      _ _  |_ _  | |_ _  | |_ _  | | |_ _  | | |_ _  | | |
%e A182244 .  _  |_  | |_  | | |_  | | |_  | | | |_  | | | |_  | | | |
%e A182244 . |_| |_|_| |_|_|_| |_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_|_|
%e A182244 .
%e A182244 .  1    4      9       11       20        23        35
%e A182244 .
%e A182244 .                                          _ _ _ _ _ _
%e A182244 .                             _ _ _       |_ _ _      |
%e A182244 .                _ _ _ _     |_ _ _|_     |_ _ _|_    |
%e A182244 .   _ _         |_ _    |    |_ _    |    |_ _    |   |
%e A182244 .  |_ _|_ _ _   |_ _|_ _|_   |_ _|_ _|_   |_ _|_ _|_  |
%e A182244 .  |_ _ _    |  |_ _ _    |  |_ _ _    |  |_ _ _    | |
%e A182244 .  |_ _ _|_  |  |_ _ _|_  |  |_ _ _|_  |  |_ _ _|_  | |
%e A182244 .  |_ _    | |  |_ _    | |  |_ _    | |  |_ _    | | |
%e A182244 .  |_ _|_  | |  |_ _|_  | |  |_ _|_  | |  |_ _|_  | | |
%e A182244 .  |_ _  | | |  |_ _  | | |  |_ _  | | |  |_ _  | | | |
%e A182244 .  |_  | | | |  |_  | | | |  |_  | | | |  |_  | | | | |
%e A182244 .  |_|_|_|_|_|  |_|_|_|_|_|  |_|_|_|_|_|  |_|_|_|_|_|_|
%e A182244 .
%e A182244 .       37           43           46           66
%e A182244 (End)
%t A182244 lex[n_]:=DeleteCases[Sort@PadRight[Reverse /@ IntegerPartitions@n], x_ /; x==0,2];
%t A182244 A186412 = {}; l = {};
%t A182244 For[j = 1, j <= 56, j++,
%t A182244   mx = Max@lex[j][[j]]; AppendTo[l, mx];
%t A182244   For[i = j, i > 0, i--, If[l[[i]] > mx, Break[]]];
%t A182244   AppendTo[A186412, Total@Take[Reverse[First /@ lex[mx]], j - i]];
%t A182244   ];
%t A182244 Accumulate@A186412  (* _Robert Price_, Jul 25 2020 *)
%Y A182244 Partial sums of A186412. Row j has length A187219(j). Right border gives A066186.
%Y A182244 Cf. A000041, A135010, A138121, A141285, A182244, A182181, A182276, A186114, A206437, A210990.
%K A182244 nonn,tabf
%O A182244 1,2
%A A182244 _Omar E. Pol_, Apr 23 2012