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A370981 Triangle T(n, k), n >= 0, k = 0..n, read and filled in the greedy way by rows with distinct nonnegative integers, such that for any n > 0 and any k in 0..n, T(n, k) is congruent modulo n to T(n-1, k-1) (provided that k > 0) or to T(n-1, k) (provided that k < n).

%I A370981 #11 Mar 10 2024 15:11:36
%S A370981 0,1,2,3,4,6,9,7,10,12,5,11,14,8,16,15,20,19,13,18,21,27,26,25,31,24,
%T A370981 30,33,34,40,32,17,38,23,37,47,42,48,56,41,22,39,29,45,55,51,57,65,50,
%U A370981 49,58,66,36,28,46,61,67,35,60,59,68,76,86,78,88,96
%N A370981 Triangle T(n, k), n >= 0, k = 0..n, read and filled in the greedy way by rows with distinct nonnegative integers, such that for any n > 0 and any k in 0..n, T(n, k) is congruent modulo n to T(n-1, k-1) (provided that k > 0) or to T(n-1, k) (provided that k < n).
%C A370981 This sequence can be seen as a two-dimensional variant of A125717.
%C A370981 Will every integer appear in the sequence?
%H A370981 Rémy Sigrist, <a href="/A370981/b370981.txt">Table of n, a(n) for n = 0..10010</a> (rows for n = 0..140 flattened)
%H A370981 Rémy Sigrist, <a href="/A370981/a370981.png">Colored representation of the first 500 rows</a>
%H A370981 Rémy Sigrist, <a href="/A370981/a370981.gp.txt">PARI program</a>
%e A370981 Triangle T(n, k) begins:
%e A370981                          0
%e A370981                        1   2
%e A370981                      3   4   6
%e A370981                    9   7  10  12
%e A370981                  5  11  14   8  16
%e A370981               15  20  19  13  18  21
%e A370981             27  26  25  31  24  30  33
%e A370981           34  40  32  17  38  23  37  47
%e A370981         42  48  56  41  22  39  29  45  55
%e A370981       51  57  65  50  49  58  66  36  28  46
%e A370981     61  67  35  60  59  68  76  86  78  88  96
%e A370981   72  83  79  71  70  81  43  53  64  44  52  63
%o A370981 (PARI) See Links section.
%Y A370981 Cf. A125717.
%K A370981 nonn,tabl
%O A370981 0,3
%A A370981 _Rémy Sigrist_, Mar 06 2024