|
|
A204621
|
|
Triangle read by rows: coordinator triangle for lattice A*_n.
|
|
2
|
|
|
1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 6, 16, 6, 1, 1, 7, 22, 22, 7, 1, 1, 8, 29, 64, 29, 8, 1, 1, 9, 37, 93, 93, 37, 9, 1, 1, 10, 46, 130, 256, 130, 46, 10, 1, 1, 11, 56, 176, 386, 386, 176, 56, 11, 1, 1, 12, 67, 232, 562, 1024, 562, 232, 67, 12, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
FORMULA
|
T(n, k) = Sum_{i=0..min(k,n-k)} binomial(n+1,i). [Wang and Yu, Theorem 4.1] - Eric M. Schmidt, Dec 07 2017
|
|
EXAMPLE
|
Triangle begins:
1
1 1
1 4 1
1 5 5 1
1 6 16 6 1
1 7 22 22 7 1
1 8 29 64 29 8 1
1 9 37 93 93 37 9 1
1 10 46 130 256 130 46 10 1
1 11 56 176 386 386 176 56 11 1
...
|
|
MATHEMATICA
|
T[n_, k_] := Sum[Binomial[n+1, i] , {i, 0, Min[k, n-k]}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Dec 14 2018 *)
|
|
PROG
|
(GAP) Flat(List([0..10], n->List([0..n], k->Sum([0..Minimum(k, n-k)], i->Binomial(n+1, i))))); # Muniru A Asiru, Dec 14 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|