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Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation starts with 2 and has exactly n runs.
2

%I #7 Mar 15 2024 21:30:40

%S 2,8,6,26,7,19,80,18,20,57,242,22,21,59,172,728,24,23,60,173,516,2186,

%T 25,55,61,177,518,1549,6560,54,56,64,178,519,1550,4647,19682,67,58,65,

%U 181,520,1554,4649,13942

%N Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation starts with 2 and has exactly n runs.

%C Every positive integer occurs in this array or A370924.

%e Corner:

%e 2 8 26 80 242 728 2186

%e 6 7 18 22 24 25 54

%e 19 20 21 23 55 56 58

%e 57 59 60 61 64 65 69

%e 172 173 177 178 181 182 183

%e 516 518 519 520 532 533 534

%e 1549 1550 1554 1555 1558 1559 1560

%t d[n_] := First[IntegerDigits[n, 3]];

%t a[n_] := a[n] = Select[Range[30000],

%t d[#] == 2 && Length[Split[IntegerDigits[#, 3]]] == n &];

%t t[n_, k_] := a[n][[k]];

%t Grid[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]] (* array *)

%t Table[t[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* sequence *)

%Y Cf. A007089, A157671, A370893, A370924.

%K nonn,base,tabl

%O 1,1

%A _Clark Kimberling_, Mar 13 2024