OFFSET
1,1
COMMENTS
The formula yields squares of hypotenuses of right triangles having integer side lengths (A000404), but with duplicates (cf. A024508) and not in increasing order. - M. F. Hasler, Apr 05 2016
LINKS
Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened
FORMULA
a(n, k) = n^2 + k^2, 1 <= k <= n.
EXAMPLE
a(3,2)=13 because 3^2+2^2=13.
Triangle begins:
2;
5, 8;
10, 13, 18;
17, 20, 25, 32;
26, 29, 34, 41, 50;
37, 40, 45, 52, 61, 72;
50, 53, 58, 65, 74, 85, 98;
65, 68, 73, 80, 89, 100, 113, 128;
82, 85, 90, 97, 106, 117, 130, 145, 162;
101, 104, 109, 116, 125, 136, 149, 164, 181, 200; ...
- Vincenzo Librandi, Apr 30 2014
MATHEMATICA
t[n_, k_]:=n^2 + k^2; Table[t[n, k], {n, 11}, {k, n}]//Flatten (* Vincenzo Librandi, Apr 30 2014 *)
PROG
(Haskell)
a070216 n k = a070216_tabl !! (n-1) !! (k-1)
a070216_row n = a070216_tabl !! (n-1)
a070216_tabl = zipWith (zipWith (\u v -> (u + v) `div` 2))
a215630_tabl a215631_tabl
-- Reinhard Zumkeller, Nov 11 2012
(Magma) [n^2+k^2: k in [1..n], n in [1..15]]; // Vincenzo Librandi, Apr 30 2014
(PARI) T(n, k) = n^2+k^2;
for (n=1, 10, for(k=1, n, print1(T(n, k), ", "))) \\ Altug Alkan, Mar 24 2016
CROSSREFS
KEYWORD
AUTHOR
Charles Northup (cnorthup(AT)esc6.net), May 07 2002
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Sep 25 2002
Edited and corrected by M. F. Hasler, Apr 05 2016
STATUS
approved