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A307435 Number of partitions of n into parts whose bitwise AND equals 0. 2
1, 0, 0, 1, 1, 3, 5, 9, 11, 18, 27, 38, 53, 75, 102, 137, 178, 238, 313, 406, 528, 677, 865, 1093, 1382, 1742, 2181, 2717, 3377, 4175, 5146, 6320, 7737, 9454, 11516, 13986, 16950, 20473, 24682, 29672, 35631, 42663, 50992, 60807, 72399, 86008, 102027, 120793 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1024

Wikipedia, Bitwise operation

Wikipedia, Partition (number theory)

EXAMPLE

a(0) = 1: the empty partition.

a(3) = 1: 21.

a(4) = 1: 211.

a(5) = 3: 2111, 221, 41.

a(6) = 5: 21111, 2211, 321, 411, 42.

a(7) = 9: 211111, 22111, 2221, 3211, 4111, 421, 43, 52, 61.

a(8) = 11: 2111111, 221111, 22211, 32111, 3221, 41111, 4211, 422, 431, 521, 611.

a(9) = 18: 21111111, 2211111, 222111, 22221, 321111, 32211, 3321, 411111, 42111, 4221, 4311, 432, 441, 5211, 522, 6111, 621, 81.

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0),

     `if`(i<1, 0, b(n, i-1, k)+b(n-i, min(n-i, i), Bits[And](i, k))))

    end:

a:= n-> b(n$2, `if`(n=0, 0, 2^ilog2(2*n)-1)):

seq(a(n), n=0..50);

CROSSREFS

Column k=0 of A307432.

Sequence in context: A100456 A059819 A074986 * A123328 A226175 A091945

Adjacent sequences:  A307432 A307433 A307434 * A307436 A307437 A307438

KEYWORD

nonn,base

AUTHOR

Alois P. Heinz, Apr 08 2019

STATUS

approved

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Last modified October 23 16:46 EDT 2019. Contains 328373 sequences. (Running on oeis4.)