This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A093995 #43 Nov 09 2024 01:12:19
%S A093995 1,4,4,9,9,9,16,16,16,16,25,25,25,25,25,36,36,36,36,36,36,49,49,49,49,
%T A093995 49,49,49,64,64,64,64,64,64,64,64,81,81,81,81,81,81,81,81,81,100,100,
%U A093995 100,100,100,100,100,100,100,100,121,121,121,121,121,121,121,121,121,121,121
%N A093995 n^2 appears n times, triangle read by rows.
%C A093995 Row sums give A000578.
%C A093995 Triangle sums give A000537.
%H A093995 Reinhard Zumkeller, <a href="/A093995/b093995.txt">Rows n = 1..120 of triangle, flattened</a>
%F A093995 T(n, k) = n^2, 1<=k<=n.
%F A093995 a(n) = floor(sqrt(2*n - 1) + 1/2)^2. - _Ridouane Oudra_, Jun 18 2019
%F A093995 From _G. C. Greubel_, Dec 27 2021: (Start)
%F A093995 T(n, n-k) = T(n, k).
%F A093995 Sum_{k=1..floor(n/2)} T(n, k) = [n=1] + A265645(n+1).
%F A093995 Sum_{k=1..floor(n/2)} T(n-k, k) = (1/48)*n*(n-1)*(7*(2*n-1) + 3*(-1)^n).
%F A093995 T(2*n-1, n) = A016754(n).
%F A093995 T(2*n, n) = A016742(n). (End)
%e A093995 First few rows of the triangle are:
%e A093995 1;
%e A093995 4, 4;
%e A093995 9, 9, 9;
%e A093995 16, 16, 16, 16;
%e A093995 25, 25, 25, 25, 25;
%e A093995 36, 36, 36, 36, 36, 36;
%e A093995 49, 49, 49, 49, 49, 49, 49;
%e A093995 ...
%p A093995 seq(seq(n^2, i=1..n), n=1..20); # _Ridouane Oudra_, Jun 18 2019
%t A093995 Flatten[Table[Table[n^2,{n}],{n,11}]] (* _Harvey P. Dale_, Feb 18 2011 *)
%t A093995 Table[PadRight[{},n,n^2],{n,12}]//Flatten (* _Harvey P. Dale_, Jun 28 2023 *)
%o A093995 (Haskell)
%o A093995 a093995 n k = a093995_tabl !! (n-1) !! (k-1)
%o A093995 a093995_row n = a093995_tabl !! (n-1)
%o A093995 a093995_tabl = zipWith replicate [1..] $ tail a000290_list
%o A093995 a093995_list = concat a093995_tabl
%o A093995 -- _Reinhard Zumkeller_, Nov 11 2012, Mar 18 2011, Oct 17 2010
%o A093995 (Magma) [n^2: k in [1..n], n in [1..13]]; // _G. C. Greubel_, Dec 27 2021
%o A093995 (Sage) flatten([[n^2 for k in (1..n)] for n in (1..13)]) # _G. C. Greubel_, Dec 27 2021
%o A093995 (Python)
%o A093995 from math import isqrt
%o A093995 def A093995(n): return ((m:=isqrt(k:=n<<1))+(k>m*(m+1)))**2 # _Chai Wah Wu_, Nov 07 2024
%Y A093995 Cf. A000290, A000537, A000578, A016742, A016754, A127733, A199332, A265645.
%K A093995 nonn,tabl
%O A093995 1,2
%A A093995 _Reinhard Zumkeller_, May 24 2004
%E A093995 Edited by _N. J. A. Sloane_, Jul 03 2008 at the suggestion of _R. J. Mathar_
%E A093995 Definition clarified by _N. J. A. Sloane_, Nov 09 2024