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A199332
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Triangle read by rows, where even numbered rows contain the nonsquares (cf. A000037) and odd rows contain replicated squares.
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8
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1, 2, 3, 4, 4, 4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 10, 11, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 38
(list;
table;
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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An approximation of the Euler-Mascheroni constant by rational numbers: the sum ((-1)^(n+1) * Sum_{k=1..n} (1/T(n,k))) converges to gamma, cf. Pólya-Szegő reference.
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REFERENCES
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G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 1, sec. 2, Problem 19.2., page 51.
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LINKS
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EXAMPLE
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1: 1 1
2: 2 3 2 .. 3
3: 4 4 4 4
4: 5 6 7 8 5 .. 8
5: 9 9 9 9 9 9
6: 10 11 12 13 14 15 10 .. 15
7: 16 16 16 16 16 16 16 16
8: 17 18 19 20 21 22 23 24 17 .. 24
9: 25 25 25 25 25 25 25 25 25 25 .
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MATHEMATICA
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t[n_, k_] := If[OddQ[n], (n+1)^2/4, n^2/4 + k]; Flatten[ Table[ t[n, k], {n, 1, 12}, {k, 1, n}]](* Jean-François Alcover, Dec 05 2011 *)
Flatten[Table[If[IntegerQ[Sqrt[n]], Table[n, {2*Sqrt[n]-1}], n], {n, 40}]] (* Harvey P. Dale, Nov 11 2013 *)
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PROG
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(Haskell)
a199332 n k = a199332_tabl !! (n-1) !! (k-1)
a199332_row n = a199332_tabl !! (n-1)
a199332_list = concat a199332_tabl
a199332_tabl = f [1..] [1..] where
f (x:xs) ys'@(y:ys) | odd x = (replicate x y) : f xs ys
| even x = us : f xs vs
where (us, vs) = splitAt x ys'
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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