# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a332284 Showing 1-1 of 1 %I A332284 #12 Jan 21 2024 10:57:22 %S A332284 0,0,0,0,0,0,1,2,4,6,12,18,28,42,62,86,123,168,226,306,411,534,704, %T A332284 908,1165,1492,1898,2384,3011,3758,4673,5799,7168,8792,10804,13192, %U A332284 16053,19505,23633,28497,34367,41283,49470,59188,70675,84113,100048,118689,140533 %N A332284 Number of integer partitions of n whose first differences (assuming the last part is zero) are not unimodal. %C A332284 A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence. %H A332284 Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400 %H A332284 Eric Weisstein's World of Mathematics, Unimodal Sequence. %e A332284 The a(6) = 1 through a(11) = 18 partitions: %e A332284 (2211) (331) (431) (441) (541) (551) %e A332284 (22111) (3311) (4311) (3322) (641) %e A332284 (22211) (32211) (3331) (4331) %e A332284 (221111) (33111) (4411) (4421) %e A332284 (222111) (33211) (5411) %e A332284 (2211111) (42211) (33221) %e A332284 (43111) (33311) %e A332284 (222211) (44111) %e A332284 (322111) (52211) %e A332284 (331111) (322211) %e A332284 (2221111) (332111) %e A332284 (22111111) (422111) %e A332284 (431111) %e A332284 (2222111) %e A332284 (3221111) %e A332284 (3311111) %e A332284 (22211111) %e A332284 (221111111) %t A332284 unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]]; %t A332284 Table[Length[Select[IntegerPartitions[n],!unimodQ[Differences[Append[#,0]]]&]],{n,30}] %Y A332284 The complement is counted by A332283. %Y A332284 The strict version is A332286. %Y A332284 The Heinz numbers of these partitions are A332287. %Y A332284 Non-unimodal permutations are A059204. %Y A332284 Non-unimodal compositions are A115981. %Y A332284 Non-unimodal normal sequences appear to be A328509. %Y A332284 Partitions with non-unimodal run-lengths are A332281. %Y A332284 Heinz numbers of partitions with non-unimodal run-lengths are A332282. %Y A332284 Cf. A001523, A007052, A332280, A332285, A332288, A332579, A332638, A332639, A332640, A332642. %K A332284 nonn %O A332284 0,8 %A A332284 _Gus Wiseman_, Feb 20 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE