OFFSET
1,2
LINKS
Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened
FORMULA
T(n, k) = n^2, 1<=k<=n.
a(n) = floor(sqrt(2*n - 1) + 1/2)^2. - Ridouane Oudra, Jun 18 2019
From G. C. Greubel, Dec 27 2021: (Start)
T(n, n-k) = T(n, k).
Sum_{k=1..floor(n/2)} T(n, k) = [n=1] + A265645(n+1).
Sum_{k=1..floor(n/2)} T(n-k, k) = (1/48)*n*(n-1)*(7*(2*n-1) + 3*(-1)^n).
T(2*n-1, n) = A016754(n).
T(2*n, n) = A016742(n). (End)
EXAMPLE
First few rows of the triangle are:
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, 49, 49, 49;
...
MAPLE
seq(seq(n^2, i=1..n), n=1..20); # Ridouane Oudra, Jun 18 2019
MATHEMATICA
Flatten[Table[Table[n^2, {n}], {n, 11}]] (* Harvey P. Dale, Feb 18 2011 *)
Table[PadRight[{}, n, n^2], {n, 12}]//Flatten (* Harvey P. Dale, Jun 28 2023 *)
PROG
(Haskell)
a093995 n k = a093995_tabl !! (n-1) !! (k-1)
a093995_row n = a093995_tabl !! (n-1)
a093995_tabl = zipWith replicate [1..] $ tail a000290_list
a093995_list = concat a093995_tabl
-- Reinhard Zumkeller, Nov 11 2012, Mar 18 2011, Oct 17 2010
(Magma) [n^2: k in [1..n], n in [1..13]]; // G. C. Greubel, Dec 27 2021
(Sage) flatten([[n^2 for k in (1..n)] for n in (1..13)]) # G. C. Greubel, Dec 27 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, May 24 2004
EXTENSIONS
Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar
STATUS
approved