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A070216
Triangle T(n, k) = n^2 + k^2, 1 <= k <= n, read by rows.
10
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
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
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