A176210 - OEIS

%I #10 Sep 08 2022 08:45:52

%S 3,4,5,6,3,3,7,4,3,8,5,3,4,4,9,6,3,5,4,3,3,3,10,7,3,6,4,5,5,4,3,3,11,

%T 8,3,7,4,6,5,5,3,3,4,4,3,12,9,3,8,4,7,5,6,6,6,3,3,5,4,3,4,4,4,3,3,3,3,

%U 13,10,3,9,4,8,5,7,6,7,3,3,6,4,3,5,5,3,5,4,4,4,3,3,3

%N Triangle read by rows in which row n (n>=3) lists those partitions of n with every part > 2.

%C Each partition is listed in nonincreasing order.

%C The partitions in each row are listed in decreasing lexicographic order.

%C Also the numbers of vertices of the connected components of the 2-regular simple graphs on n vertices.

%H J. S. Kimberley, <a href="/A176210/b176210.txt">Rows 3..39 of A176210 triangle, flattened</a> [b-file corrected by _N. J. A. Sloane_, Oct 05 2010]

%e For n in {0,1,2} there are no parts; so those rows are empty.

%e 3 (one partition only)

%e 4 (one partition only)

%e 5 (one partition only)

%e 6; 3, 3

%e 7; 4, 3

%e 8; 5, 3; 4, 4

%e 9; 6, 3; 5, 4; 3, 3, 3

%e 10; 7, 3; 6, 4; 5, 5; 4, 3, 3

%e 11; 8, 3; 7, 4; 6, 5; 5, 3, 3; 4, 4, 3

%e 12; 9, 3; 8, 4; 7, 5; 6, 6; 6, 3, 3; 5, 4, 3; 4, 4, 4; 3, 3, 3, 3

%e 13; 10, 3; 9, 4; 8, 5; 7, 6; 7, 3, 3; 6, 4, 3; 5, 5, 3; 5, 4, 4; 4, 3, 3, 3

%o (Magma) &cat[ &cat RestrictedPartitions(n,{3..n}):n in [1..13]];

%Y The number of partitions in each row is A008483.

%Y The length of each row is A177739.

%Y The same ordering is used in A080577 and A138136 (for other orderings see A036036 and A036037).

%K easy,nonn,tabf

%O 3,1

%A _Vladimir Shevelev_, Apr 12 2010

%E Extensively edited by _Jason Kimberley_, May 13 2010