A101417 Number of partitions of n into parts without powers of 2.

1, 0, 0, 1, 0, 1, 2, 1, 1, 3, 3, 3, 6, 5, 6, 10, 9, 12, 17, 17, 22, 28, 30, 37, 48, 52, 62, 78, 86, 103, 127, 141, 166, 201, 227, 266, 317, 358, 417, 492, 560, 647, 757, 860, 991, 1153, 1309, 1503, 1738, 1971, 2257, 2594, 2941, 3356, 3843, 4351, 4948, 5644, 6382, 7240

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{j>=1} (1-x^(2^j)) / Product_{i>=2} (1-x^i). - Emeric Deutsch, Mar 29 2006

Example

a(12) = #{3+3+3+3, 6+3+3, 6+6, 7+5, 9+3, 12} = 6.
From Gus Wiseman, Jan 07 2019: (Start)
The a(3) = 1 through a(14) = 5 integer partitions (A = 10, ..., E = 14):
  (3)  (5)  (6)   (7)  (53)  (9)    (A)   (B)    (C)     (D)    (E)
            (33)             (63)   (55)  (65)   (66)    (76)   (77)
                             (333)  (73)  (533)  (75)    (A3)   (95)
                                                 (93)    (553)  (B3)
                                                 (633)   (733)  (653)
                                                 (3333)         (5333)
(End)

Maple

g:= product(1-x^(2^j), j=0..15)/product(1-x^i, i=1..75): gser:= series(g, x=0, 62): seq(coeff(gser, x, n), n=0..59); # Emeric Deutsch, Mar 29 2006

Mathematica

Table[Length[Select[IntegerPartitions[n], And@@Not/@IntegerQ/@Log[2, #]&]], {n, 20}] (* Gus Wiseman, Jan 07 2019 *)

Crossrefs

Cf. A000041, A018819, A000123.

Cf. A087897, A102430, A276431, A321346, A323053, A323092, A323093.

Sequence in context: A283672 A053268 A284828 * A318660 A301502 A260056

Adjacent sequences: A101414 A101415 A101416 * A101418 A101419 A101420

Keyword

nonn

Author

Reinhard Zumkeller, Jan 16 2005

Status

approved