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A199332 Triangle read by rows, where even numbered rows contain the nonsquares (cf. A000037) and odd rows contain replicated squares. 8
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)
OFFSET

1,2

COMMENTS

An approximation of the Euler-Mascheroni constant by rational numbers:

sum ((-1)^(n+1) * sum (1/T(n,k): k=1..n)) converges to gamma, cf. Polya-Szego reference.

REFERENCES

G. Polya and G. Szego, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 1, §2, Problem 19.2., page 51.

LINKS

Reinhard Zumkeller, Rows n=1..150 of triangle, flattened

Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant

Wikipedia, Euler-Mascheroni constant

EXAMPLE

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 .

MATHEMATICA

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 *)

PROG

(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'

CROSSREFS

Cf. A000290 & A002620 (central terms),  A199771 (row sums).

Sequence in context: A135414 A099479 A120508 * A029085 A087875 A195848

Adjacent sequences:  A199329 A199330 A199331 * A199333 A199334 A199335

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Nov 23 2011

STATUS

approved

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Last modified August 21 13:36 EDT 2017. Contains 290890 sequences.