A325876 Number of strict Golomb partitions of n.
1, 1, 1, 2, 2, 3, 3, 5, 6, 6, 9, 11, 10, 15, 17, 18, 24, 29, 27, 38, 43, 47, 53, 67, 67, 84, 87, 102, 113, 137, 131, 167, 179, 204, 213, 261, 263, 315, 327, 377, 413, 476, 472, 564, 602, 677, 707, 820, 845, 969, 1027, 1131, 1213, 1364, 1413, 1596, 1700, 1858
Offset: 0
Keywords
Examples
The a(2) = 1 through a(11) = 11 partitions (A = 10, B = 11): (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (21) (31) (32) (42) (43) (53) (54) (64) (65) (41) (51) (52) (62) (63) (73) (74) (61) (71) (72) (82) (83) (421) (431) (81) (91) (92) (521) (621) (532) (A1) (541) (542) (631) (632) (721) (641) (731) (821)
Links
- Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500
Crossrefs
Programs
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Mathematica
Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@Subtract@@@Subsets[Union[#],{2}]&]],{n,0,30}]
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Python
from collections import Counter from itertools import combinations from sympy.utilities.iterables import partitions def A325876(n): return sum(1 for p in partitions(n) if max(list(Counter(abs(d[0]-d[1]) for d in combinations(list(Counter(p).elements()),2)).values()),default=1)==1)-(n&1^1) if n else 1 # Chai Wah Wu, Sep 17 2023
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