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A377667
Square array read by antidiagonals upwards: T(i,j) is the smallest number m such that the symmetric representation of sigma, SRS(m), has maximum width 3, consists of i parts and has 2*j occurrences of maximum width 3 in its width pattern (row m of A341969).
1
60, 10728, 210, 315, 7620, 810, 495, 1155, 840456, 2070, 525, 28158, 945, 88410, 7290, 1275, 1995, 30555, 1575, 408150, 12810, 1287, 2625, 3003, 22365, 2835, 1313010, 45450, 6105, 3315, 10659, 18975, 382305, 11385
OFFSET
1,1
COMMENTS
When m is odd and SRS(m) has maximum width 3 then SRS(m) has at least 3 parts because the first and last parts of SRS(m) consist of a single leg of width 1. Therefore, the first two rows of the table contain only even numbers. The numbers in the third row appear to be odd and divisible by 15.
EXAMPLE
a(8) = T(3,2) = 1155 is the smallest example whose symmetric representation of sigma has 3 parts and 4 counts of width 3 in its width pattern.
Upper left hand section of table T(i, j) = m, numbers m <= 10^7, Columns j indicate 2j occurrences of width 3 in the width pattern of m. T(2, 7) > 10^7.
i\j| 1 2 3 4 5 6 7 8 ...
---------------------------------------------------------------------
1 | 60 210 810 2070 7290 12810 45450 146610
2 | 10728 7620 840456 88410 408150 1313010 >10^7 8596710
3 | 315 1155 945 1575 2835 11385 8505 40095
4 | 495 28158 30555 22365 382305 296835 256095 199395
5 | 525 1995 3003 18975 15147 23925 14553 186219
6 | 1275 2625 10659 35217 132957 818363 312039 1760031
7 | 1287 3315 13125 37107 44289 195415 482937 258687
8 | 6105 3861 31875 65625 132153 149435 807495 1426113
9 | 3591 10773 56889 66861 254065 797979 319599 2199477
10 | 6783 16443 57477 222999 417175 1540875 768339 4670991
11 | 18963 35397 106191 965979 1025973 1770783 2489151 7547427
12 | 90801 58653 47481 1223365 2449785 4600617 ... ...
13 | 152019 107457 817209 2213253 1740081 4310481
14 | 257397 297087 410571 3086349 3552213 5170055
15 | 335225 815409 1360989 2079609 ... ...
16 | 1523319 2600283 1642557 2563239
17 | 1473725 1739375 4116777 ...
18 | 4008125 3826625 3687475
19 | 7576085 7937875 ...
... ... ...
MATHEMATICA
(* widthPattern[ ] and its support functions are defined in A376829 *)
t377667[b_, {r_, c_}] := Module[{t=ConstantArray[0, {r, c}], k, wP, c3, p3}, For[k=1, k<=b, k++, wP=widthPattern[k]; If[Max[wP]==3, c3=Count[wP, 3]; If[EvenQ[c3]&&c3<=2c, c3/=2; p3=Length[Select[SplitBy[wP, #!=0&], First[#]!=0&]]; If[p3<=r &&t[[p3, c3]]==0, t[[p3, c3]]=k]]]]; t]
t377667[1540875, {10, 6}] (* complete 10 x 6 upper left hand section of table *)
CROSSREFS
Subsequence of A376829.
Sequence in context: A146498 A003750 A001525 * A309996 A146513 A269883
KEYWORD
nonn,tabl,more,changed
AUTHOR
Hartmut F. W. Hoft, Nov 03 2024
STATUS
approved