OFFSET
1,2
COMMENTS
EXAMPLE
The 10x10 initial submatrix of table T(n,k):
n\k | 2 3 4 5 6 7 8 9 10 11 ...
------------------------------------------------------------------
1 | 3 9 21 63 147 357 903 2499 6069 13915
2 | 5 15 27 81 171 399 987 2709 6321 14847
3 | 7 25 33 99 189 441 1029 2793 6325 15125
4 | 11 35 39 117 207 483 1113 2961 6783 15141
5 | 13 45 51 153 243 513 1197 3025 6875 15351
6 | 17 49 55 165 261 567 1239 3087 6909 15729
7 | 19 77 57 195 275 609 1265 3249 7011 16023
8 | 23 91 65 231 279 621 1281 3339 7203 16611
9 | 29 121 69 255 297 651 1375 3381 7353 16779
10| 31 135 75 273 333 729 1407 3591 7581 17157
...
a(9) = 25 = T(3,3) since only 9 and 15 are smaller odd numbers whose symmetric representation of sigma consists of three parts. All 3 parts of the symmetric representation of sigma for 9 and for 25 have width 1 while the center part for that of 15 has width 2.
MATHEMATICA
(* function a341969 is defined in A341969 *)
sArray[b_, pMax_] := Module[{list=Table[{}, pMax+1], i, p}, For[i=3, i<=b, i+=2, p=Length[Select[SplitBy[a341969[i], #!=0&], #[[1]]!=0&]]; If[p<=pMax+1&&Length[list[[p]]]<pMax, AppendTo[list[[p]], i]]]; If[MatrixQ[Rest[list]], Transpose[Rest[list]], "square matrix not filled"]]
parts[n_] := n-row[n-1](row[n-1]+1)/2
rank[n_] := row[n-1]-parts[n]+2
a346969[sMatrix_, aD_] := Prepend[Map[sMatrix[[ rank[#], parts[#]]] &, Range[aD (aD + 1)/2]], 1] /; MatrixQ[sMatrix] && aD <= Length[sMatrix]
m40000=sArray[40000, 11] (* entire 11x11 table filled *)
a346969[m40000, 11] (* sequence data: 1 followed by the first 11 antidiagonals in the table *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Hartmut F. W. Hoft, Oct 06 2021
STATUS
approved