A070216 Triangle T(n, k) = n^2 + k^2, 1 <= k <= n, read by rows.

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, 122, 125, 130, 137, 146, 157

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.

T(n,k) = (A215630(n,k) + A215631(n,k)) / 2, 1 <= k <=n. - Reinhard Zumkeller, Nov 11 2012

T(n,k) = A002024(n,k)^2 + A002260(n,k)^2. - David Rabahy, Mar 24 2016

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

Not a permutation of sequence A000404 (which has no duplicates).

Cf. A002522 (left edge), A001105 (right edge), A219054 (row sums).

Sequence in context: A096691 A202057 A263651 * A100829 A030713 A219222

Adjacent sequences: A070213 A070214 A070215 * A070217 A070218 A070219

Keyword

easy,nonn,tabl

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