OFFSET
1,2
LINKS
Stefano Spezia, First 150 antidiagonals of the table, flattened
FORMULA
EXAMPLE
The table T starts in row n = 1 with columns k >= 1 as:
1 2 3 4 5 6 7 8 9 ...
4 1 12 2 20 3 28 4 36 ...
9 18 1 36 45 2 63 72 3 ...
16 4 48 1 80 12 112 2 144 ...
25 50 75 100 1 150 175 200 225 ...
36 9 4 18 180 1 252 36 12 ...
49 98 147 196 245 294 1 392 441 ...
64 16 192 4 320 48 448 1 576 ...
81 162 9 324 405 18 567 648 1 ...
...
The triangle X(n, k) begins
n\k| 1 2 3 4 5 6 7 8 9
---+----------------------------------------------------
1 | 1
2 | 4 2
3 | 9 1 3
4 | 16 18 12 4
5 | 25 4 1 2 5
6 | 36 50 48 36 20 6
7 | 49 9 75 1 45 3 7
8 | 64 98 4 100 80 2 28 8
9 | 81 16 147 18 1 12 63 4 9
...
MAPLE
a := (n, k) -> (n+1-k)^2*k/gcd(n+1-k, k)^3: seq(seq(a(n, k), k = 1 .. n), n = 1 .. 12)
MATHEMATICA
T[n_, k_]:=n^2*k/GCD[n, k]^3; Flatten[Table[T[n-k+1, k], {n, 12}, {k, n}]]
PROG
(GAP) Flat(List([1..12], n->List([1..n], k->(n+1-k)^2*k/GcdInt(n+1-k, k)^3)));
(Magma) [[(n+1-k)^2*k/Gcd(n+1-k, k)^3: k in [1..n]]: n in [1..12]]; // triangle output
(Maxima) sjoin(v, j) := apply(sconcat, rest(join(makelist(j, length(v)), v)))$ display_triangle(n) := for i from 1 thru n do disp(sjoin(makelist((i+1-j)^2*j/gcd(i+1-j, j)^3, j, 1, i), " ")); display_triangle(12);
(PARI)
T(n, k) = (n+1-k)^2*k/gcd(n+1-k, k)^3;
tabl(nn) = for(i=1, nn, for(j=1, i, print1(T(i, j), ", ")); print);
tabl(12) \\ triangle output
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Dec 15 2018
STATUS
approved