

A342097


Number of strict integer partitions of n with no adjacent parts having quotient >= 2.


37



1, 1, 1, 1, 2, 1, 2, 2, 3, 3, 3, 3, 4, 6, 6, 7, 8, 8, 9, 11, 13, 15, 18, 20, 24, 25, 29, 32, 39, 42, 48, 54, 63, 72, 81, 89, 102, 116, 132, 147, 165, 187, 210, 238, 264, 296, 329, 371, 414, 465, 516, 580, 644, 722, 803, 897, 994, 1108, 1229, 1367, 1512, 1678
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OFFSET

1,5


COMMENTS

The decapitation of such a partition (delete the greatest part) is termwise greater than its negated firstdifferences.


LINKS

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..400


EXAMPLE

The a(1) = 1 through a(16) = 7 partitions (A..G = 10..16):
1 2 3 4 5 6 7 8 9 A B C D E F G
32 43 53 54 64 65 75 76 86 87 97
432 532 74 543 85 95 96 A6
643 653 654 754
743 753 853
5432 6432 6532
7432


MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&And@@Thread[Differences[#]<Rest[#]]&]], {n, 30}]


CROSSREFS

The case of equality (all adjacent parts having quotient 2) is A154402.
The multiplicative version is A342083 or A342084.
The nonstrict version allowing quotients of 2 exactly is A342094.
The version allowing quotients of 2 exactly is A342095.
The nonstrict version is A342096.
The reciprocal version is A342098.
A000009 counts strict partitions.
A000929 counts partitions with no adjacent parts having quotient < 2.
A003114 counts partitions with adjacent parts differing by more than 1.
A034296 counts partitions with adjacent parts differing by at most 1.
Cf. A027193, A001055, A001227, A003242, A167606, A337135, A342085.
Sequence in context: A132203 A158925 A262868 * A259357 A031265 A029202
Adjacent sequences: A342094 A342095 A342096 * A342098 A342099 A342100


KEYWORD

nonn


AUTHOR

Gus Wiseman, Mar 02 2021


STATUS

approved



