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A181229 T(n,k)=Number of length n sequences p(i=0..n-1) with 0<=p(i)<=i and having exactly k maxima.

%I A181229 #5 Jul 22 2025 08:37:32
%S A181229 1,0,2,0,0,6,0,0,0,21,0,0,0,3,79,0,0,0,0,41,311,0,0,0,0,0,383,1265,0,
%T A181229 0,0,0,0,26,3073,5275,0,0,0,0,0,0,702,22835,22431,0,0,0,0,0,0,0,11734,
%U A181229 162517,96900,0,0,0,0,0,0,0,476,156976,1127399,424068,0,0,0,0,0,0,0,0,20956
%N A181229 T(n,k)=Number of length n sequences p(i=0..n-1) with 0<=p(i)<=i and having exactly k maxima.
%C A181229 Table starts
%C A181229 ............1...............0.................0..................0
%C A181229 ............2...............0.................0..................0
%C A181229 ............6...............0.................0..................0
%C A181229 ...........21...............3.................0..................0
%C A181229 ...........79..............41.................0..................0
%C A181229 ..........311.............383................26..................0
%C A181229 .........1265............3073...............702..................0
%C A181229 .........5275...........22835.............11734................476
%C A181229 ........22431..........162517............156976..............20956
%C A181229 ........96900.........1127399...........1847636.............541960
%C A181229 .......424068.........7700835..........20046784...........10783530
%C A181229 ......1876143........52118506.........205891684..........183084580
%C A181229 ......8377299.......350902046........2034977036.........2796467584
%C A181229 .....37704042......2356532130.......19567350334........39641212284
%C A181229 ....170870106.....15813455692......184421027812.......532014841490
%C A181229 ....779058843....106160717591.....1712803733352......6852097042820
%C A181229 ...3571051579....713555194577....15736451922346.....85509456576162
%C A181229 ..16447100702...4804401287757...143435108141199...1041222110654522
%C A181229 ..76073821946..32414156949765..1299841823088167..12436416067831144
%C A181229 .353224531663.219174260505645.11730670902611152.146290172122139436
%H A181229 R. H. Hardin, <a href="/A181229/b181229.txt">Table of n, a(n) for n=1..10000</a>
%e A181229 All solutions for n=5 with k=2 maxima
%e A181229 ..0..1..0..0..1....0..1..0..0..2....0..1..0..0..3....0..1..0..0..4
%e A181229 ..0..1..0..2..0....0..1..0..2..1....0..1..0..2..2....0..1..0..2..3
%e A181229 ..0..1..0..2..4....0..1..0..1..0....0..1..0..1..1....0..1..0..1..2
%e A181229 ..0..1..0..1..3....0..1..0..1..4....0..1..0..3..0....0..1..0..3..1
%e A181229 ..0..1..0..3..2....0..1..0..3..3....0..1..0..3..4....0..0..1..0..1
%e A181229 ..0..0..1..0..2....0..0..1..0..3....0..0..1..0..4....0..0..2..0..1
%e A181229 ..0..0..2..0..2....0..0..2..0..3....0..0..2..0..4....0..0..2..1..2
%e A181229 ..0..0..2..1..3....0..0..2..1..4....0..1..1..0..1....0..1..1..0..2
%e A181229 ..0..1..1..0..3....0..1..1..0..4....0..1..2..0..1....0..1..2..0..2
%e A181229 ..0..1..2..0..3....0..1..2..0..4....0..1..2..1..2....0..1..2..1..3
%e A181229 ..0..1..2..1..4
%Y A181229 Column 1 is A033321
%K A181229 nonn,tabl
%O A181229 1,3
%A A181229 _R. H. Hardin_ Oct 10 2010