OFFSET
1,2
COMMENTS
Also triangle read by rows: T(j,k) = sum of all parts in the k-th region of the last section of the set of partitions of j. See Example section. For more information see A135010. - Omar E. Pol, Nov 26 2011
For the definition of "region" see A206437. - Omar E. Pol, Aug 19 2013
EXAMPLE
Contribution from Omar E. Pol, Nov 26 2011 (Start):
Written as a triangle:
1;
3;
5;
2,9;
3,12;
2,6,3,20;
3,7,4,25;
2,6,3,13,5,4,38;
3,7,4,14,3,9,5,49;
2,6,3,13,5,4,23,4,10,6,5,69;
3,7,4,14,3,9,5,27,5,4,15,7,6,87;
2,6,3,13,5,4,23,4,10,6,5,39,3,9,5,19,4,12,7,6,123;
(End)
From Omar E. Pol, Aug 18 2013: (Start)
Illustration of initial terms (first seven regions):
. _ _ _ _ _
. _ _ _ |_ _ _ _ _|
. _ _ _ _ |_ _ _| |_ _|
. _ _ |_ _ _ _| |_|
. _ _ _ |_ _| |_ _| |_|
. _ _ |_ _ _| |_| |_|
. _ |_ _| |_| |_| |_|
. |_| |_| |_| |_| |_|
.
. 1 3 5 2 9 3 12
.
(End)
MATHEMATICA
lex[n_]:=DeleteCases[Sort@PadRight[Reverse /@ IntegerPartitions@n], x_ /; x==0, 2];
A186412 = {}; l = {};
For[j = 1, j <= 50, 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]];
];
A186412 (* Robert Price, Jul 25 2020 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Aug 12 2011
STATUS
approved