cp's OEIS Frontend

A342097 Number of strict integer partitions of n with no adjacent parts having quotient >= 2.

%I A342097 #11 Jan 29 2022 04:20:25
%S A342097 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,
%T A342097 42,48,54,63,72,81,89,102,116,132,147,165,187,210,238,264,296,329,371,
%U A342097 414,465,516,580,644,722,803,897,994,1108,1229,1367,1512,1678
%N A342097 Number of strict integer partitions of n with no adjacent parts having quotient >= 2.
%C A342097 The decapitation of such a partition (delete the greatest part) is term-wise greater than its negated first-differences.
%H A342097 Fausto A. C. Cariboni, <a href="/A342097/b342097.txt">Table of n, a(n) for n = 1..400</a>
%e A342097 The a(1) = 1 through a(16) = 7 partitions (A..G = 10..16):
%e A342097   1  2  3  4  5   6  7   8   9    A    B   C    D    E     F     G
%e A342097               32     43  53  54   64   65  75   76   86    87    97
%e A342097                              432  532  74  543  85   95    96    A6
%e A342097                                                 643  653   654   754
%e A342097                                                      743   753   853
%e A342097                                                      5432  6432  6532
%e A342097                                                                  7432
%t A342097 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&And@@Thread[Differences[-#]<Rest[#]]&]],{n,30}]
%Y A342097 The case of equality (all adjacent parts having quotient 2) is A154402.
%Y A342097 The multiplicative version is A342083 or A342084.
%Y A342097 The non-strict version allowing quotients of 2 exactly is A342094.
%Y A342097 The version allowing quotients of 2 exactly is A342095.
%Y A342097 The non-strict version is A342096.
%Y A342097 The reciprocal version is A342098.
%Y A342097 A000009 counts strict partitions.
%Y A342097 A000929 counts partitions with no adjacent parts having quotient < 2.
%Y A342097 A003114 counts partitions with adjacent parts differing by more than 1.
%Y A342097 A034296 counts partitions with adjacent parts differing by at most 1.
%Y A342097 Cf. A027193, A001055, A001227, A003242, A167606, A337135, A342085.
%K A342097 nonn
%O A342097 1,5
%A A342097 _Gus Wiseman_, Mar 02 2021