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A342095 Number of strict integer partitions of n with no adjacent parts having quotient > 2.

%I A342095 #11 Jan 29 2022 04:20:36
%S A342095 1,1,2,1,2,3,3,2,4,4,6,7,6,8,10,9,13,16,17,20,25,26,29,36,40,45,55,61,
%T A342095 69,81,90,103,119,132,154,176,196,225,254,282,323,364,403,458,519,582,
%U A342095 655,735,822,922,1035,1153,1290,1441,1600,1788,1997,2217,2468
%N A342095 Number of strict integer partitions of n with no adjacent parts having quotient > 2.
%C A342095 The decapitation of such a partition (delete the greatest part) is term-wise greater than or equal to its negated first-differences.
%H A342095 Fausto A. C. Cariboni, <a href="/A342095/b342095.txt">Table of n, a(n) for n = 1..400</a>
%e A342095 The a(1) = 1 through a(15) = 10 partitions (A..F = 10..15):
%e A342095   1  2  3   4  5   6    7    8   9    A     B     C     D     E     F
%e A342095         21     32  42   43   53  54   64    65    75    76    86    87
%e A342095                    321  421      63   532   74    84    85    95    96
%e A342095                                  432  4321  542   543   643   653   A5
%e A342095                                             632   642   742   743   654
%e A342095                                             5321  5421  6421  842   753
%e A342095                                                   6321        5432  843
%e A342095                                                               7421  6432
%e A342095                                                                     8421
%e A342095                                                                     54321
%t A342095 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&And@@Thread[Differences[-#]<=Rest[#]]&]],{n,30}]
%Y A342095 The reciprocal version (no adjacent parts having quotient < 2) is A000929.
%Y A342095 The case of equality (all adjacent parts having quotient 2) is A154402.
%Y A342095 The multiplicative version is A342085 or A337135.
%Y A342095 The non-strict version is A342094.
%Y A342095 The non-strict version without quotients of 2 exactly is A342096.
%Y A342095 The version without quotients of 2 exactly is A342097.
%Y A342095 A000009 counts strict partitions.
%Y A342095 A003114 counts partitions with adjacent parts differing by more than 1.
%Y A342095 A034296 counts partitions with adjacent parts differing by at most 1.
%Y A342095 Cf. A001055, A001227, A003242, A056239, A167606, A342083, A342084.
%K A342095 nonn
%O A342095 1,3
%A A342095 _Gus Wiseman_, Mar 02 2021