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A233968
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Number of steps between two valleys at height 0 in the infinite Dyck path in which the k-th ascending line segment has A141285(k) steps and the k-th descending line segment has A194446(k) steps, k >= 1.
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3
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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
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1,1
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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Illustration of initial terms as a dissection of a minimalist diagram of regions of the set of partitions of n, for n = 1..6:
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. 2 4 6 12 16 30
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Also using the elements from the above diagram we can draw an infinite Dyck path in which the n-th odd-indexed segment has A141285(n) up-steps and the n-th even-indexed segment has A194446(n) down-steps. Note that the n-th 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,...
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CROSSREFS
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Cf. A000041, A006128, A135010, A138137, A139582, A141285, A182699, A182709, A186412, A194446, A194447, A193870, A206437, A207779, A211009, A211978, A211992, A220517, A225600, A225610, A228109, A228110, A229946.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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