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A193331 Triangle of edge counts for the (n,k)-Turan graphs. 2
0, 0, 1, 0, 2, 3, 0, 4, 5, 6, 0, 6, 8, 9, 10, 0, 9, 12, 13, 14, 15, 0, 12, 16, 18, 19, 20, 21, 0, 16, 21, 24, 25, 26, 27, 28, 0, 20, 27, 30, 32, 33, 34, 35, 36, 0, 25, 33, 37, 40, 41, 42, 43, 44, 45, 0, 30, 40, 45, 48, 50, 51, 52, 53, 54, 55, 0, 36, 48, 54, 57, 60, 61, 63, 64, 64, 65, 66 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The triangle of t(n,k) begins:

0

0, 1

0, 2,  3

0, 4,  5,  6

0, 6,  8,  9, 10

0, 9, 12, 13, 14, 15

LINKS

Reinhard Zumkeller, Rows n=1..100 of triangle, flattened

P. Erdos, R. J. Faudree, C. C. Rousseau, Extremal problems involving vertices and edges on odd cycles, Disc. Math. 101 (1992) 23-31

Eric Weisstein's World of Mathematics, Turan Graph

Eric Weisstein's World of Mathematics, Turans Theorem

FORMULA

t(n,k) = floor((k-1)*n^2/(2*k)).

MATHEMATICA

Flatten[Table[Floor[(k - 1) n^2/(2k)], {n, 20}, {k, n}]]

PROG

(Haskell)

a193331 n k = a193331_tabl !! (n-1) !! (k-1)

a193331_tabl = map a193331_row [1..]

a193331_row n = zipWith div (map (* n^2) [0..n-1]) (map (2 *) [1..n])

-- Reinhard Zumkeller, Aug 08 2011

(PARI) T(n, k)=(k-1)*n^2\(2*k) \\ Charles R Greathouse IV, Aug 01 2016

CROSSREFS

Cf. A198787 (another version).

Sequence in context: A011150 A100112 A198787 * A091246 A271439 A133637

Adjacent sequences:  A193328 A193329 A193330 * A193332 A193333 A193334

KEYWORD

nonn,nice,tabl,easy,look

AUTHOR

Eric W. Weisstein, Jul 22 2011

STATUS

approved

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Last modified October 1 13:04 EDT 2020. Contains 337443 sequences. (Running on oeis4.)