

A233968


Number of steps between two valleys at height 0 in the infinite Dyck path in which the kth ascending line segment has A141285(k) steps and the kth descending line segment has A194446(k) steps, k >= 1.


3



2, 4, 6, 12, 16, 30, 38, 64, 84, 128, 166, 248, 314, 448, 576, 790, 1004, 1358, 1708, 2264, 2844, 3694, 4614, 5936, 7354, 9342, 11544, 14502, 17816, 22220, 27144, 33584, 40878, 50192, 60828, 74276, 89596, 108778, 130772, 157918, 189116, 227374
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OFFSET

1,1


COMMENTS



LINKS



FORMULA



EXAMPLE

Illustration of initial terms as a dissection of a minimalist diagram of regions of the set of partitions of n, for n = 1..6:
. _ _ _ _ _ _
. _ _ _ 
. _ _ __ 
. _ _  
. _ _ _ _ _   
. _ _ _  
. _ _ _ _   
. _ _   
. _ _ _    
. _ _    
. _     
.      
.
. 2 4 6 12 16 30
.
Also using the elements from the above diagram we can draw an infinite Dyck path in which the nth oddindexed segment has A141285(n) upsteps and the nth evenindexed segment has A194446(n) downsteps. Note that the nth largest peak between two valleys at height 0 is also the partition number A000041(n).
7..................................
. /\
5.................... / \ /\
. /\ / \ /\ /
3.......... / \ / \ / \/
2..... /\ / \ /\/ \ /
1.. /\ / \ /\/ \ / \ /\/
0 /\/ \/ \/ \/ \/
. 2, 4, 6, 12, 16,...
.


CROSSREFS

Cf. A000041, A006128, A135010, A138137, A139582, A141285, A182699, A182709, A186412, A194446, A194447, A193870, A206437, A207779, A211009, A211978, A211992, A220517, A225600, A225610, A228109, A228110, A229946.


KEYWORD

nonn


AUTHOR



STATUS

approved



