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A370924 Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation starts with 1 and has exactly n runs.

%I A370924 #8 Mar 15 2024 05:10:11
%S A370924 1,4,3,13,5,10,40,9,11,30,121,12,15,32,91,364,14,16,33,92,273,1093,17,
%T A370924 28,34,96,275,820,3280,27,29,46,97,276,821,2460,9841,36,31,47,100,277,
%U A370924 825,2462,7381,29524,39,35,48,101,289,826,2463,7382,22143
%N A370924 Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation starts with 1 and has exactly n runs.
%C A370924 Every positive integer occurs in this array or A370925.
%e A370924 Corner:
%e A370924     1    4   13   40  121  364  1093  3280
%e A370924     3    5    9   12   14   17    27    36
%e A370924    10   11   15   16   28   29    31    35
%e A370924    30   32   33   34   46   47    48    50
%e A370924    91   92   96   97  100  101   102   104
%e A370924   273  275  276  277  289  290   291   293
%e A370924   820  821  825  826  829  830   831   833
%t A370924 d[n_] := First[IntegerDigits[n, 3]];
%t A370924 a[n_] := a[n] = Select[Range[30000],
%t A370924 d[#] == 1 && Length[Split[IntegerDigits[#, 3]]] == n &];
%t A370924 t[n_, k_] := a[n][[k]];
%t A370924 Grid[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]] (* array *)
%t A370924 Table[t[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* sequence *)
%Y A370924 Cf. A007089, A043555, A132141, A370893, A370925.
%K A370924 nonn,base,tabl
%O A370924 1,2
%A A370924 _Clark Kimberling_, Mar 13 2024