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%I #10 Jan 27 2022 20:46:41
%S 1,1,2,3,4,6,9,12,16,24,30,40,54,69,89,118,146,187,239,297,372,468,
%T 575,711,880,1075,1314,1610,1947,2359,2864,3438,4135,4973,5936,7090,
%U 8466,10044,11922,14144,16698,19704,23249,27306,32071,37639,44019,51457,60113
%N Number of integer partitions of n with no difference -2.
%H Gus Wiseman, <a href="/A069916/a069916.txt">Sequences counting and ranking partitions and compositions by their differences and quotients</a>.
%e The a(1) = 1 through a(7) = 12 partitions:
%e (1) (2) (3) (4) (5) (6) (7)
%e (11) (21) (22) (32) (33) (43)
%e (111) (211) (41) (51) (52)
%e (1111) (221) (222) (61)
%e (2111) (321) (322)
%e (11111) (411) (511)
%e (2211) (2221)
%e (21111) (3211)
%e (111111) (4111)
%e (22111)
%e (211111)
%e (1111111)
%t Table[Length[Select[IntegerPartitions[n],FreeQ[Differences[#],-2]&]],{n,0,30}]
%Y Heinz number rankings are in parentheses below.
%Y The version for no difference 0 is A000009.
%Y The version for subsets of prescribed maximum is A005314.
%Y The version for all differences < -2 is A025157, non-strict A116932.
%Y The version for all differences > -2 is A034296, strict A001227.
%Y The opposite version is A072670.
%Y The version for no difference -1 is A116931 (A319630), strict A003114.
%Y The multiplicative version is A350837 (A350838), strict A350840.
%Y The strict case is A350844.
%Y The complement for quotients is counted by A350846 (A350845).
%Y A000041 = integer partitions.
%Y A027187 = partitions of even length.
%Y A027193 = partitions of odd length (A026424).
%Y A323092 = double-free partitions (A320340), strict A120641.
%Y A325534 = separable partitions (A335433).
%Y A325535 = inseparable partitions (A335448).
%Y A350839 = partitions with a gap and conjugate gap (A350841).
%Y Cf. A000070, A000929, A001511, A003242, A007359, A018819, A040039, A045690, A045691, A101417, A154402, A323093.
%K nonn
%O 0,3
%A _Gus Wiseman_, Jan 20 2022
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