A325110 Number of strict integer partitions of n with no binary containments.

1, 1, 1, 2, 1, 2, 2, 5, 2, 3, 2, 6, 3, 6, 7, 15, 8, 10, 6, 13, 6, 10, 12, 23, 13, 16, 16, 26, 21, 30, 37, 60, 43, 52, 42, 60, 42, 50, 54, 81, 59, 60, 66, 80, 74, 86, 108, 145, 119, 125, 126, 144, 134, 140, 170, 208, 189, 193, 221, 248, 253, 292, 323, 435, 392

Offset

0,4

Comments

A pair of positive integers is a binary containment if the positions of 1's in the reversed binary expansion of the first are a subset of the positions of 1's in the reversed binary expansion of the second.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600

Example

The a(1) = 1 through a(12) = 3 partitions (A = 10, B = 11, C = 12):
  (1)  (2)  (3)   (4)  (5)   (6)   (7)    (8)   (9)   (A)   (B)    (C)
            (21)       (41)  (42)  (43)   (53)  (63)  (82)  (65)   (84)
                                   (52)         (81)        (83)   (93)
                                   (61)                     (92)
                                   (421)                    (A1)
                                                            (821)

Mathematica

binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&stableQ[#, SubsetQ[binpos[#1], binpos[#2]]&]&]], {n, 0, 30}]

Crossrefs

Cf. A019565, A050315, A267610, A267700.

Cf. A325101, A325106, A325107, A325108, A325109, A325119.

Sequence in context: A079318 A050315 A128978 * A357888 A145862 A364536

Adjacent sequences: A325107 A325108 A325109 * A325111 A325112 A325113

Keyword

nonn

Author

Gus Wiseman, Mar 28 2019

Status

approved