A214725 Smallest number expressible as a sum of 9 cubes (including 0) in n ways.

0, 8, 35, 72, 133, 189, 216, 224, 280, 376, 411, 496, 533, 472, 568, 624, 712, 720, 784, 783, 908, 946, 992, 945, 1062, 1072, 1081, 1107, 1153, 1161, 1224, 1288, 1376, 1377, 1449, 1459, 1547, 1496, 1504, 1593, 1592, 1712, 1719, 1648, 1783, 1800, 1837, 1864

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Fred Richman, Lists the ways of writing i as a sum of 9 cubes (including 0)

Example

a(1) = 0: [0,0,0,0,0,0,0,0,0].
a(2) = 8: [0,0,0,0,0,0,0,0,2], [0,1,1,1,1,1,1,1,1].
a(3) = 35: [0,0,0,0,0,0,0,2,3], [0,0,1,1,1,2,2,2,2], [1,1,1,1,1,1,1,1,3].
a(7) = 216: [0,0,0,0,0,0,0,0,6], [0,1,1,1,2,2,2,4,5], [0,0,1,1,2,3,3,3,5], [1,2,2,3,3,3,3,3,4], [0,0,0,2,2,2,4,4,4], [0,3,3,3,3,3,3,3,3], [0,0,0,0,0,0,3,4,5].

Maple

b:= proc(n, i, t) option remember;
      `if`(n=0, 1, `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(i^3>n, 0, b(n-i^3, i, t-1))))
    end:
a:= proc(n) local k;
      for k from 0 while b(k, isqrt(k), 9)<>n do od; k
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Jul 26 2012

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, If[i < 1 || t < 1, 0, b[n, i - 1, t] + If[i^3 > n, 0, b[n - i^3, i, t - 1]]]];
a[n_] := Module[{k}, For[k = 0, b[k, Floor@Sqrt[k], 9] != n, k++]; k];
Array[a, 20] (* Jean-François Alcover, Nov 21 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A281147 A373484 A217187 * A136016 A257454 A305672

Adjacent sequences: A214722 A214723 A214724 * A214726 A214727 A214728

Keyword

nonn

Author

Claudio Meller, Jul 26 2012

Extensions

More terms from Alois P. Heinz, Jul 26 2012

Status

approved