|
|
A131067
|
|
Triangle read by rows: T(n,k) = 7*binomial(n,k) - 6 for 0 <= k <= n.
|
|
11
|
|
|
1, 1, 1, 1, 8, 1, 1, 15, 15, 1, 1, 22, 36, 22, 1, 1, 29, 64, 64, 29, 1, 1, 36, 99, 134, 99, 36, 1, 1, 43, 141, 239, 239, 141, 43, 1, 1, 50, 190, 386, 484, 386, 190, 50, 1, 1, 57, 246, 582, 876, 876, 582, 246, 57, 1, 1, 64, 309, 834, 1464, 1758, 1464, 834, 309, 64, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Row sums = A131068: (1, 2, 10, 32, 82, 188, 406, ...), the binomial transform of (1, 1, 7, 7, 7, ...).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: G(t,z) = (1-z-t*z+7*t*z^2)/((1-z)*(1-t*z)*(1-z-t*z)). - Emeric Deutsch, Jun 20 2007
|
|
EXAMPLE
|
First few rows of the triangle:
1;
1, 1;
1, 8, 1;
1, 15, 15, 1;
1, 22, 36, 22, 1;
1, 29, 64, 64, 29, 1;
...
|
|
MAPLE
|
T := proc (n, k) if k <= n then 7*binomial(n, k)-6 else 0 end if end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # Emeric Deutsch, Jun 20 2007
|
|
MATHEMATICA
|
Table[7*Binomial[n, k] -6, {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Mar 12 2020 *)
|
|
PROG
|
(Magma) [7*Binomial(n, k) -6: k in [0..n], n in [0..10]]; // G. C. Greubel, Mar 12 2020
(Sage) [[7*binomial(n, k) -6 for k in (0..n)] for n in (0..10)] # G. C. Greubel, Mar 12 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|