cp's OEIS Frontend

A333191 Number of compositions of n whose run-lengths are either strictly increasing or strictly decreasing.

%I A333191 #11 May 19 2020 06:53:14
%S A333191 1,1,2,2,5,8,10,18,24,29,44,60,68,100,130,148,201,256,310,396,478,582,
%T A333191 736,898,1068,1301,1594,1902,2288,2750,3262,3910,4638,5510,6538,7686,
%U A333191 9069,10670,12560,14728,17170,20090,23462,27292,31710,36878,42704,49430
%N A333191 Number of compositions of n whose run-lengths are either strictly increasing or strictly decreasing.
%C A333191 A composition of n is a finite sequence of positive integers summing to n.
%H A333191 Giovanni Resta, <a href="/A333191/b333191.txt">Table of n, a(n) for n = 0..1000</a>
%F A333191 a(n > 0) = 2*A333192(n) - A000005(n).
%e A333191 The a(1) = 1 through a(7) = 18 compositions:
%e A333191   (1)  (2)   (3)    (4)     (5)      (6)       (7)
%e A333191        (11)  (111)  (22)    (113)    (33)      (115)
%e A333191                     (112)   (122)    (114)     (133)
%e A333191                     (211)   (221)    (222)     (223)
%e A333191                     (1111)  (311)    (411)     (322)
%e A333191                             (1112)   (1113)    (331)
%e A333191                             (2111)   (3111)    (511)
%e A333191                             (11111)  (11112)   (1114)
%e A333191                                      (21111)   (1222)
%e A333191                                      (111111)  (2221)
%e A333191                                                (4111)
%e A333191                                                (11113)
%e A333191                                                (11122)
%e A333191                                                (22111)
%e A333191                                                (31111)
%e A333191                                                (111112)
%e A333191                                                (211111)
%e A333191                                                (1111111)
%t A333191 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],Or[Less@@Length/@Split[#],Greater@@Length/@Split[#]]&]],{n,0,15}]
%Y A333191 The non-strict version is A332835.
%Y A333191 The case of partitions is A333190.
%Y A333191 Unimodal compositions are A001523.
%Y A333191 Strict compositions are A032020.
%Y A333191 Partitions with distinct run-lengths are A098859.
%Y A333191 Partitions with strictly increasing run-lengths are A100471.
%Y A333191 Partitions with strictly decreasing run-lengths are A100881.
%Y A333191 Partitions with weakly decreasing run-lengths are A100882.
%Y A333191 Partitions with weakly increasing run-lengths are A100883.
%Y A333191 Compositions with equal run-lengths are A329738.
%Y A333191 Compositions whose run-lengths are unimodal are A332726.
%Y A333191 Compositions whose run-lengths are unimodal or co-unimodal are A332746.
%Y A333191 Compositions whose run-lengths are neither incr. nor decr. are A332833.
%Y A333191 Compositions that are neither increasing nor decreasing are A332834.
%Y A333191 Compositions with weakly increasing run-lengths are A332836.
%Y A333191 Compositions that are strictly incr. or strictly decr. are A333147.
%Y A333191 Compositions with strictly increasing run-lengths are A333192.
%Y A333191 Cf. A059204, A072706, A329398, A329744, A329766, A332641, A332726, A332831, A332745, A333149.
%K A333191 nonn
%O A333191 0,3
%A A333191 _Gus Wiseman_, May 17 2020
%E A333191 Terms a(26) and beyond from _Giovanni Resta_, May 19 2020