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A216053 a(n) is the position of the last two-tuple within the reverse lexicographic set of partitions of 2n and 2n+1, with a(1)-a(n) representing the positions of every 2-tuple partition of 2n and 2n+1. 5

%I

%S 2,3,5,8,13,20,31,46,68,98,140,196,273,374,509,685,916,1213,1598,2088,

%T 2715,3507,4509,5764,7339,9297,11733,14743,18461,23026,28630,35472,

%U 43821,53964,66274,81157,99134,120771,146786,177971,215309,259892,313066,376327

%N a(n) is the position of the last two-tuple within the reverse lexicographic set of partitions of 2n and 2n+1, with a(1)-a(n) representing the positions of every 2-tuple partition of 2n and 2n+1.

%H J. Stauduhar, <a href="/A216053/b216053.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ exp(Pi*sqrt(2*n/3)) / (Pi*2^(3/2)*sqrt(n)). - _Vaclav Kotesovec_, May 24 2018

%F a(n) = A330661(2n,2) = A330661(2n+1,2). - _Alois P. Heinz_, Feb 20 2020

%e With n = 3, 2n = 6. The partitions of 6 are {{6}, {5,1}, {4,2}, {4,1,1}, {3,3}, {3,2,1}, {3,1,1,1}, {2,2,2}, {2,2,1,1}, {2,1,1,1,1}, {1,1,1,1,1,1}}. The last 2-tuple is located at position 5. The positions of all 2-tuples are 2, 3, and 5.

%t RecurrenceTable[{a[n+1] == a[n] + PartitionsP[(n)], a[1] == 2}, a, {n, 1, 44}]

%Y A diagonal of A181187.

%Y Cf. A080577, A330661, A332706.

%K nonn

%O 1,1

%A _J. Stauduhar_, Oct 12 2012

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Last modified July 29 11:53 EDT 2021. Contains 346346 sequences. (Running on oeis4.)