|
|
A131240
|
|
T(n,k) = 2*A046854(n,k) - I.
|
|
2
|
|
|
1, 2, 1, 2, 2, 1, 2, 4, 2, 1, 2, 4, 6, 2, 1, 2, 6, 6, 8, 2, 1, 2, 6, 12, 8, 10, 2, 1, 2, 8, 12, 20, 10, 12, 2, 1, 2, 8, 20, 20, 30, 12, 14, 2, 1, 2, 10, 20, 40, 30, 42, 14, 16, 2, 1, 2, 10, 30, 40, 70, 42, 56, 16, 18, 2, 1, 2, 12, 30, 70, 70, 112, 56, 72, 18, 20, 2, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Row sums = A001595: (1, 3, 5, 9, 15, 25, 41, 67, ...).
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = 2*A046854(n,k) - Identity matrix, where A046854 = Pascal's triangle with repeats by columns.
|
|
EXAMPLE
|
First few rows of the triangle:
1;
2, 1;
2, 2, 1;
2, 4, 2, 1;
2, 4, 6, 2, 1;
2, 6, 6, 8, 2, 1;
2, 6, 12, 8, 10, 2, 1;
...
|
|
MATHEMATICA
|
Table[If[k==n, 1, 2*Binomial[Floor[(n+k)/2], k]], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 12 2019 *)
|
|
PROG
|
(PARI) T(n, k) = if(k==n, 1, 2*binomial((n+k)\2, k));
(Magma) [k eq n select 1 else 2*Binomial(Floor((n+k)/2), k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 12 2019
(Sage)
def T(n, k):
if (k==n): return 1
else: return 2*binomial(floor((n+k)/2), k)
[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jul 12 2019
(GAP)
T:= function(n, k)
if k=n then return 1;
else return 2*Binomial(Int((n+k)/2), k);
fi;
end;
Flat(List([0..12], n-> List([0..n], k-> T(n, k)))); # G. C. Greubel, Jul 12 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|