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A182244
Sum of all parts of the shell model of partitions of A135010 with n regions.
9
1, 4, 9, 11, 20, 23, 35, 37, 43, 46, 66, 69, 76, 80, 105, 107, 113, 116, 129, 134, 138, 176, 179, 186, 190, 204, 207, 216, 221, 270, 272, 278, 281, 294, 299, 303, 326, 330, 340, 346, 351, 420, 423, 430, 434, 448, 451, 460, 465, 492, 497, 501, 516, 523, 529, 616
OFFSET
1,2
FORMULA
a(A000041(k)) = A066186(k), k >= 1.
EXAMPLE
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.
Written as a triangle begins:
1;
4;
9;
11, 20;
23, 35;
37, 43, 46, 66;
69, 76, 80,105;
107,113,116,129,134,138,176;
179,186,190,204,207,216,221,270;
272,278,281,294,299,303,326,330,340,346,351,420;
423,430,434,448,451,460,465,492,497,501,516,523,529,616;
...
From Omar E. Pol, Aug 08 2013: (Start)
Illustration of initial terms:
. _ _ _ _ _
. _ _ _ |_ _ _ |
. _ _ _ _ |_ _ _|_ |_ _ _|_ |
. _ _ |_ _ | |_ _ | |_ _ | |
. _ _ _ |_ _|_ |_ _|_ | |_ _|_ | |_ _|_ | |
. _ _ |_ _ | |_ _ | |_ _ | | |_ _ | | |_ _ | | |
. _ |_ | |_ | | |_ | | |_ | | | |_ | | | |_ | | | |
. |_| |_|_| |_|_|_| |_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_|_|
.
. 1 4 9 11 20 23 35
.
. _ _ _ _ _ _
. _ _ _ |_ _ _ |
. _ _ _ _ |_ _ _|_ |_ _ _|_ |
. _ _ |_ _ | |_ _ | |_ _ | |
. |_ _|_ _ _ |_ _|_ _|_ |_ _|_ _|_ |_ _|_ _|_ |
. |_ _ _ | |_ _ _ | |_ _ _ | |_ _ _ | |
. |_ _ _|_ | |_ _ _|_ | |_ _ _|_ | |_ _ _|_ | |
. |_ _ | | |_ _ | | |_ _ | | |_ _ | | |
. |_ _|_ | | |_ _|_ | | |_ _|_ | | |_ _|_ | | |
. |_ _ | | | |_ _ | | | |_ _ | | | |_ _ | | | |
. |_ | | | | |_ | | | | |_ | | | | |_ | | | | |
. |_|_|_|_|_| |_|_|_|_|_| |_|_|_|_|_| |_|_|_|_|_|_|
.
. 37 43 46 66
(End)
MATHEMATICA
lex[n_]:=DeleteCases[Sort@PadRight[Reverse /@ IntegerPartitions@n], x_ /; x==0, 2];
A186412 = {}; l = {};
For[j = 1, j <= 56, j++,
mx = Max@lex[j][[j]]; AppendTo[l, mx];
For[i = j, i > 0, i--, If[l[[i]] > mx, Break[]]];
AppendTo[A186412, Total@Take[Reverse[First /@ lex[mx]], j - i]];
];
Accumulate@A186412 (* Robert Price, Jul 25 2020 *)
CROSSREFS
Partial sums of A186412. Row j has length A187219(j). Right border gives A066186.
Sequence in context: A365892 A312845 A312846 * A312847 A141365 A179055
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Apr 23 2012
STATUS
approved