A308558 Triangle read by rows where T(n,k) is the number of integer partitions of n > 0 into powers of k > 0.

1, 1, 2, 1, 2, 2, 1, 4, 2, 2, 1, 4, 2, 2, 2, 1, 6, 3, 2, 2, 2, 1, 6, 3, 2, 2, 2, 2, 1, 10, 3, 3, 2, 2, 2, 2, 1, 10, 5, 3, 2, 2, 2, 2, 2, 1, 14, 5, 3, 3, 2, 2, 2, 2, 2, 1, 14, 5, 3, 3, 2, 2, 2, 2, 2, 2, 1, 20, 7, 4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 20, 7, 4, 3, 3, 2

Offset

1,3

Links

Table of n, a(n) for n=1..85.

Example

Triangle begins:
  1
  1  2
  1  2  2
  1  4  2  2
  1  4  2  2  2
  1  6  3  2  2  2
  1  6  3  2  2  2  2
  1 10  3  3  2  2  2  2
  1 10  5  3  2  2  2  2  2
  1 14  5  3  3  2  2  2  2  2
  1 14  5  3  3  2  2  2  2  2  2
  1 20  7  4  3  3  2  2  2  2  2  2
  1 20  7  4  3  3  2  2  2  2  2  2  2
Row n = 6 counts the following partitions:
  (111111)  (42)      (33)      (411)     (51)      (6)
            (222)     (3111)    (111111)  (111111)  (111111)
            (411)     (111111)
            (2211)
            (21111)
            (111111)

Mathematica

Table[If[k==1, 1, Length[Select[IntegerPartitions[n], And@@(IntegerQ[Log[k, #]]&/@#)&]]], {n, 10}, {k, n}]

Crossrefs

Same as A102430 except for the k = 1 column.

Row sums are A102431(n) + 1.

Column k = 2 is A018819.

Column k = 3 is A062051.

Cf. A000961, A001597, A007916, A008284, A023894, A052410, A101417, A112344, A323053, A323054.

Sequence in context: A373127 A363345 A344651 * A105272 A060438 A106190

Adjacent sequences: A308555 A308556 A308557 * A308559 A308560 A308561

Keyword

nonn,tabl

Author

Gus Wiseman, Jun 07 2019

Status

approved