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A115981
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The number of compositions of n which cannot be viewed as stacks.
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98
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0, 0, 0, 0, 0, 1, 5, 17, 49, 126, 303, 694, 1536, 3312, 7009, 14619, 30164, 61732, 125568, 254246, 513048, 1032696, 2074875, 4163256, 8345605, 16717996, 33473334, 66998380, 134067959, 268233386, 536599508, 1073378850, 2147000209
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OFFSET
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0,7
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COMMENTS
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A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence. A composition of n is a finite sequence of positive integers summing to n. - Gus Wiseman, Mar 05 2020
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 1 counting (212}.
a(6) = 5 counting {1212, 2112,2121,213,312}.
a(7) = 17 counting {11212, 12112,12121, 21211, 21121, 21112, 2122, 2212, 2113, 3112, 2131, 3121, 1213, 1312, 412, 214, 313}.
a(8) = 49 = 128 - 79.
a(9) = 126 = 256 - 130.
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MATHEMATICA
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unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !unimodQ[#]&]], {n, 0, 10}] (* Gus Wiseman, Mar 05 2020 *)
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CROSSREFS
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The complement is counted by A001523.
The case covering an initial interval is A332743.
The version whose negation is not unimodal either is A332870.
Non-unimodal permutations are A059204.
Non-unimodal normal sequences are A328509.
Partitions with non-unimodal run-lengths are A332281.
Numbers whose prime signature is not unimodal are A332282.
Partitions whose 0-appended first differences are not unimodal are A332284.
Non-unimodal permutations of the prime indices of n are A332671.
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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More terms from Brian Kuehn (brk158(AT)psu.edu), Apr 20 2006
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STATUS
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approved
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