OFFSET
0,7
COMMENTS
Identification of rows and columns:
Row 2, n=1: A060819,
row 3, n=2: A060819 (shifted),
row 4, n=3: A068219,
row 5, n=4: A060819 (shifted),
row 6, n=5: A060819 (shifted and multiplied by 5),
row 7, n=6: A068219 (shifted),
row 8, n=7: A060819 (shifted and multiplied by 7);
column 1, k=0: A181318,
column 2, k=1: A064038,
column 3, k=2: A198148,
column 4, k=3: A160050,
column 5, k=4: A061037,
column 6, k=5: A178242,
column 7, k=6: A217366,
column 8, k=7: A217367.
This array is the transposition of the array given by Paul Curtz in the comments in A181318.
LINKS
G. C. Greubel, Antidiagonals n=0..100 of triangle, flattened
FORMULA
t(n,k) = ((n+k)/gcd(n+k,4))*(n/gcd(n,4)).
EXAMPLE
Array begins:
0, 0, 0, 0, 0, 0, 0, ...
1, 1, 3, 1, 5, 3, 7, ...
1, 3, 1, 5, 3, 7, 2, ...
9, 3, 15, 9, 21, 6, 27, ...
1, 5, 3, 7, 2, 9, 5, ...
25, 15, 35, 10, 45, 25, 55, ...
9, 21, 6, 27, 15, 33, 9, ...
49, 14, 63, 35, 77, 21, 91, ...
...
Triangle begins:
0;
1, 0;
1, 1, 0;
9, 3, 3, 0;
1, 3, 1, 1, 0;
25, 5, 15, 5, 5, 0;
9, 15, 3, 9, 3, 3, 0;
49, 21, 35, 7, 21, 7, 7, 0;
4, 14, 6, 10, 2, 6, 2, 2, 0;
81, 18, 63, 27, 45, 9, 27, 9, 9, 0;
25, 45, 10, 35, 15, 25, 5, 15, 5, 5, 0;
121, 55, 99, 22, 77, 33, 55, 11, 33, 11, 11, 0;
9, 33, 15, 27, 6, 21, 9, 15, 3, 9, 3, 3, 0;
...
MATHEMATICA
t[n_, k_] := (n+k)/GCD[n+k, 4]*n/GCD[n, 4]; Table[t[n-k, k], {n, 0, 12}, {k, 0, n}] // Flatten
PROG
(Magma) /* As triangle: */ [[(n-k)/GCD(n-k, 4)*n/GCD(n, 4): k in [0..n]]: n in [0..12]]; // Bruno Berselli, Jun 13 2013
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jean-François Alcover, Jun 12 2013
STATUS
approved