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A336725 A(n,k) is the n-th number that is a sum of k positive k-th powers; square array A(n,k), n>=1, k>=1, read by antidiagonals. 10
1, 2, 2, 3, 5, 3, 4, 10, 8, 4, 5, 19, 17, 10, 5, 6, 36, 34, 24, 13, 6, 7, 69, 67, 49, 29, 17, 7, 8, 134, 132, 98, 64, 36, 18, 8, 9, 263, 261, 195, 129, 84, 43, 20, 9, 10, 520, 518, 388, 258, 160, 99, 55, 25, 10, 11, 1033, 1031, 773, 515, 321, 247, 114, 62, 26, 11, 12, 2058, 2056, 1542, 1028, 642, 384, 278, 129, 66, 29, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Antidiagonals n = 1..141, flattened

EXAMPLE

Square array A(n,k) begins:

   1,  2,  3,   4,   5,   6,    7,    8,    9,   10, ...

   2,  5, 10,  19,  36,  69,  134,  263,  520, 1033, ...

   3,  8, 17,  34,  67, 132,  261,  518, 1031, 2056, ...

   4, 10, 24,  49,  98, 195,  388,  773, 1542, 3079, ...

   5, 13, 29,  64, 129, 258,  515, 1028, 2053, 4102, ...

   6, 17, 36,  84, 160, 321,  642, 1283, 2564, 5125, ...

   7, 18, 43,  99, 247, 384,  769, 1538, 3075, 6148, ...

   8, 20, 55, 114, 278, 734,  896, 1793, 3586, 7171, ...

   9, 25, 62, 129, 309, 797, 2193, 2048, 4097, 8194, ...

  10, 26, 66, 164, 340, 860, 2320, 6568, 4608, 9217, ...

MAPLE

A:= proc() local l, w, A; l, w, A:= proc() [] end, proc() [] end,

      proc(n, k) option remember; local b; b:=

        proc(x, y) option remember; `if`(x=0, {0}, `if`(y<1, {},

          {b(x, y-1)[], map(t-> t+l(k)[y], b(x-1, y))[]}))

        end;

        while nops(w(k)) < n do forget(b);

          l(k):= [l(k)[], (nops(l(k))+1)^k];

          w(k):= sort([select(h-> h<l(k)[-1], b(k, nops(l(k))))[]])

        od; w(k)[n]

      end; A

    end():

seq(seq(A(n, 1+d-n), n=1..d), d=1..12);

CROSSREFS

Columns k=1-11 give: A000027, A000404, A003072, A003338, A003350, A003362, A003374, A003386, A003398, A004810, A004822.

Rows n=1-3 give: A000027, A052944, A145071.

Main diagonal gives A000337.

Cf. A336820.

Sequence in context: A210565 A125101 A208519 * A210232 A047666 A285935

Adjacent sequences:  A336722 A336723 A336724 * A336726 A336727 A336728

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Aug 01 2020

STATUS

approved

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Last modified November 30 02:42 EST 2020. Contains 338781 sequences. (Running on oeis4.)