OFFSET
2,1
COMMENTS
Tree-able degree sequences are degree sequences that can be realized as trees [Stern].
The partitions of n-2 are given in nondecreasing order of length/lex.
LINKS
Washington Bomfim, Table of n, a(n) for n = 2..9297 (Rows n = 2..27, flattened)
Samuel Stern, The Tree of Trees: on methods for finding all non-isomorphic tree-realizations of degree sequences, Honors Thesis, Wesleyan University, 2017.
EXAMPLE
Triangle T(n,k) begins:
n/k 1 2 3 ...
2 4;
3 12;
4 40, 36;
5 112, 120, 108;
6 352, 336, 400, 360, 324;
7 832, 1056, 1120, 1008, 1200, 1080, 972;
8 2176, 2496, 3520, 3136, 3168, 3360, 4000, 3024, 3600, 3240, 2916;
...
Row 5 is 112, 120, 108 because prime(1) = 2, prime(2) = 3, prime(3) = 5, and prime(4) = 7. The tree-able degree sequences of 5 nodes, related tree realization and encode are given below.
[4, 1, 1, 1, 1] o 7*2*2*2*2 = 112.
( ) ( )
o o o o
[3, 2, 1, 1, 1] o 5*3*2*2*2 = 120.
/ | \
o--o o o
[2, 2, 2, 1, 1] o--o--o--o--o 3*3*3*2*2 = 108.
PROG
(PARI) \\ Gives row n of triangle, n >= 2.
Row(n)={my(j=1, V=vector(numbpart(n-2))); forpart(P=n-2,
V[j] = prod(k = 1, #P, prime(P[k] + 1)); V[j] <<= (n-#P); j++ ); V };
CROSSREFS
KEYWORD
AUTHOR
Washington Bomfim, Jun 02 2021
STATUS
approved