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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.

%I A330587 #16 Feb 11 2021 11:14:25
%S A330587 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,
%T A330587 20,11,33,41,49,44,30,26,24,14,46,43,55,56,59,40,37,34,22,67,52,64,58,
%U A330587 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
%N 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.
%H A330587 Alois P. Heinz, <a href="/A330587/b330587.txt">Antidiagonals n = 1..365, flattened</a>
%e A330587 Square array A(n,k) begins:
%e A330587    0,  3,  6, 13,  21,  23,  27,  33,  46,  67, ...
%e A330587    1,  7, 10, 16,  31,  38,  41,  43,  52,  70, ...
%e A330587    2,  9, 12, 19,  36,  49,  55,  64,  78,  91, ...
%e A330587    4, 15, 18, 29,  44,  56,  58,  76,  88,  93, ...
%e A330587    5, 17, 25, 30,  59,  62,  73,  84,  90,  98, ...
%e A330587    8, 20, 26, 40,  61,  72,  75,  87, 117, 139, ...
%e A330587   11, 24, 37, 50,  69,  79,  85, 121, 124, 154, ...
%e A330587   14, 34, 39, 51,  82, 102, 118, 142, 155, 157, ...
%e A330587   22, 35, 47, 66,  97, 110, 133, 180, 190, 202, ...
%e A330587   28, 53, 57, 74, 106, 116, 164, 183, 197, 205, ...
%p A330587 b:= proc() 0 end:
%p A330587 g:= proc(n) option remember; local t;
%p A330587       t:= `if`(n<2, n, b(g(n-1))+b(g(n-2)));
%p A330587       b(t):= b(t)+1; t
%p A330587     end:
%p A330587 f:= proc(n) option remember; b(g(n)) end:
%p A330587 A:= proc() local l, t; t, l:= -1, proc() [] end;
%p A330587       proc(n,k) local h;
%p A330587         while nops(l(k))<n do t:= t+1;
%p A330587           h:= f(t); l(h):= [l(h)[], t]
%p A330587         od: l(k)[n]
%p A330587       end
%p A330587     end():
%p A330587 seq(seq(A(n, 1+d-n), n=1..d), d=1..14);
%t A330587 b[_] = 0;
%t A330587 g[n_] := g[n] = Module[{t}, t = If[n < 2, n, b[g[n - 1]] + b[g[n - 2]]]; b[t]++; t];
%t A330587 f[n_] := f[n] = b[g[n]];
%t A330587 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]]];
%t A330587 Table[Table[A[n, 1 + d - n], {n, 1, d}], {d, 1, 14}] // Flatten (* _Jean-François Alcover_, Feb 11 2021, after _Alois P. Heinz_ *)
%Y A330587 Column k=1 gives A330440.
%Y A330587 Row n=1 gives A330588.
%Y A330587 Main diagonal gives A330589.
%Y A330587 Cf. A316774, A330439.
%K A330587 nonn,tabl
%O A330587 1,2
%A A330587 _Alois P. Heinz_, Dec 18 2019