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A093995
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n^2 repeated n times, triangle read by rows.
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7
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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, 64, 64, 64, 64, 64, 64, 64, 64, 81, 81, 81, 81, 81, 81, 81, 81, 81, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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T(n, k) = n^2, 1<=k<=n.
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).
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EXAMPLE
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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;
...
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MAPLE
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MATHEMATICA
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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 *)
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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