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A320537
Square array read by antidiagonals in which T(n,k) is the n-th even number j with the property that the symmetric representation of sigma(j) has k parts.
3
2, 4, 10, 6, 14, 50, 8, 22, 70, 230, 12, 26, 98, 250, 1150, 16, 34, 110, 290, 1250, 5050, 18, 38, 130, 310, 1450, 5150, 22310, 20, 44, 154, 370, 1550, 5290, 23230, 106030, 24, 46, 170, 406, 1850, 5350, 23690, 106490, 510050, 28, 52, 182, 410, 2030, 5450, 24610, 107410, 513130, 2065450
OFFSET
1,1
COMMENTS
This is a permutation of the positive even numbers (A299174).
The union of all odd-indexed columns gives A319796, the even numbers in A071562.
The union of all even-indexed columns gives A319802, the even numbers in A071561.
EXAMPLE
From Hartmut F. W. Hoft, Oct 06 2021: (Start)
The 10x10 section of table T(n,k):
(Table with first 20 terms from Omar E. Pol)
------------------------------------------------------------------
n\k | 1 2 3 4 5 6 7 8 9 10 ...
------------------------------------------------------------------
1 | 2 10 50 230 1150 5050 22310 106030 510050 2065450
2 | 4 14 70 250 1250 5150 23230 106490 513130 2115950
3 | 6 22 98 290 1450 5290 23690 107410 520150 2126050
4 | 8 26 110 310 1550 5350 24610 110170 530150 2157850
5 | 12 34 130 370 1850 5450 25070 112010 530450 2164070
6 | 16 38 154 406 2030 5650 25250 112930 532450 2168150
7 | 18 44 170 410 2050 5750 25750 114770 534290 2176550
8 | 20 46 182 430 2150 6250 25990 115690 537050 2186650
9 | 24 52 190 434 2170 6350 26450 116150 540350 2216950
10| 28 58 238 470 2350 6550 26750 117070 544870 2219650
... (End)
MATHEMATICA
(* function a341969 is defined in A341969 *)
sArray[b_, pMax_] := Module[{list=Table[{}, pMax], i, p}, For[i=2, i<=b, i+=2, p=Length[Select[SplitBy[a341969[i], #!=0&], #[[1]]!=0&]]; If[p<=pMax&&Length[list[[p]]]<pMax, AppendTo[list[[p]], i]]]; list]
rank[n_] := n-row[n-1](row[n-1]+1)/2
parts[n_] := row[n-1]-rank[n]+2
a320537[sMatrix_, aD_] := Map[sMatrix[[rank[#], parts[#]]]&, Range[aD (aD+1)/2]]/; MatrixQ[sMatrix]&&aD<=Length[sMatrix]
m2500000=sArray[2500000, 10] (* entire 10x10 matrix needs to be computed *)
a320537[m2500000, 10] (* Sequence Data a(1..55) *)
(* Hartmut F. W. Hoft, Oct 06 2021 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Oct 15 2018
EXTENSIONS
Terms a(21) and beyond from Hartmut F. W. Hoft, Oct 06 2021
STATUS
approved