A330587 A(n,k) is the n-th index m such that A330439(m) = k; square array A(n,k), n>=1, k>=1, read by antidiagonals.

0, 3, 1, 6, 7, 2, 13, 10, 9, 4, 21, 16, 12, 15, 5, 23, 31, 19, 18, 17, 8, 27, 38, 36, 29, 25, 20, 11, 33, 41, 49, 44, 30, 26, 24, 14, 46, 43, 55, 56, 59, 40, 37, 34, 22, 67, 52, 64, 58, 62, 61, 50, 39, 35, 28, 81, 70, 78, 76, 73, 72, 69, 51, 47, 53, 32, 104, 94, 91, 88, 84, 75, 79, 82, 66, 57, 54, 42

Offset: 1

Author

Alois P. Heinz, Dec 18 2019

Keywords

• nonn
• tabl

Examples

			Square array A(n,k) begins:
   0,  3,  6, 13,  21,  23,  27,  33,  46,  67, ...
   1,  7, 10, 16,  31,  38,  41,  43,  52,  70, ...
   2,  9, 12, 19,  36,  49,  55,  64,  78,  91, ...
   4, 15, 18, 29,  44,  56,  58,  76,  88,  93, ...
   5, 17, 25, 30,  59,  62,  73,  84,  90,  98, ...
   8, 20, 26, 40,  61,  72,  75,  87, 117, 139, ...
  11, 24, 37, 50,  69,  79,  85, 121, 124, 154, ...
  14, 34, 39, 51,  82, 102, 118, 142, 155, 157, ...
  22, 35, 47, 66,  97, 110, 133, 180, 190, 202, ...
  28, 53, 57, 74, 106, 116, 164, 183, 197, 205, ...
		

Links

• Alois P. Heinz, Antidiagonals n = 1..365, flattened

Crossrefs

Column k=1 gives A330440.

Row n=1 gives A330588.

Main diagonal gives A330589.

Cf. A316774, A330439.

Programs

Maple

b:= proc() 0 end:
g:= proc(n) option remember; local t;
      t:= `if`(n<2, n, b(g(n-1))+b(g(n-2)));
      b(t):= b(t)+1; t
    end:
f:= proc(n) option remember; b(g(n)) end:
A:= proc() local l, t; t, l:= -1, proc() [] end;
      proc(n,k) local h;
        while nops(l(k))
				

Mathematica

b[_] = 0;
g[n_] := g[n] = Module[{t}, t = If[n < 2, n, b[g[n - 1]] + b[g[n - 2]]]; b[t]++; t];
f[n_] := f[n] = b[g[n]];
A[n_, k_] := Module[{l, t = -1, h}, l[_] = {}; While[Length[l[k]] < n, t++; h = f[t]; AppendTo[l[h], t]]; l[k][[n]]];
Table[Table[A[n, 1 + d - n], {n, 1, d}], {d, 1, 14}] // Flatten (* Jean-François Alcover, Feb 11 2021, after Alois P. Heinz *)