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Square array T(n, k), n, k > 0, read by antidiagonal upwards; the k-th column contains, in ascending order, the integers m such that A348330(m) = k.
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%I #8 Oct 17 2021 15:27:30

%S 1,2,3,4,5,6,8,9,7,10,16,18,14,11,12,32,36,28,22,13,15,64,72,56,44,26,

%T 17,19,128,144,112,88,52,33,20,21,256,288,224,176,104,66,40,23,24,512,

%U 576,448,352,208,132,80,45,25,27,1024,1152,896,704,416,264,160,90,50,29,30,2048,2304,1792,1408,832,528,320,180,100,57,31,34

%N Square array T(n, k), n, k > 0, read by antidiagonal upwards; the k-th column contains, in ascending order, the integers m such that A348330(m) = k.

%C When interpreted as a flat array, we have a permutation of the positive integers.

%H Rémy Sigrist, <a href="/A348356/a348356.gp.txt">PARI program for A348356</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F Sum_{i = 1..n-1} T(i, k) < T(n, k).

%F T(n, 1) = 2^(n-1).

%e Array T(n, k) begins:

%e n\k| 1 2 3 4 5 6 7 8 9 10

%e ---+-----------------------------------------------------------

%e 1| 1 3 6 10 12 15 19 21 24 27

%e 2| 2 5 7 11 13 17 20 23 25 29

%e 3| 4 9 14 22 26 33 40 45 50 57

%e 4| 8 18 28 44 52 66 80 90 100 114

%e 5| 16 36 56 88 104 132 160 180 200 228

%e 6| 32 72 112 176 208 264 320 360 400 456

%e 7| 64 144 224 352 416 528 640 720 800 912

%e 8| 128 288 448 704 832 1056 1280 1440 1600 1824

%e 9| 256 576 896 1408 1664 2112 2560 2880 3200 3648

%e 10| 512 1152 1792 2816 3328 4224 5120 5760 6400 7296

%o (PARI) See Links section.

%Y Cf. A000079, A348330, A348357.

%K nonn,tabl

%O 1,2

%A _Rémy Sigrist_, Oct 14 2021