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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 (list; table; graph; refs; listen; history; text; internal format)
 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

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Last modified June 25 01:49 EDT 2021. Contains 345445 sequences. (Running on oeis4.)