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A155940 Triangle read by rows containing Vardi's optimal solution to the glove problem. 1
1, 2, 2, 2, 3, 4, 3, 4, 4, 5, 3, 4, 5, 6, 6, 4, 5, 5, 6, 7, 7, 4, 5, 6, 7, 7, 8, 9, 5, 6, 6, 7, 8, 8, 9, 10, 5, 6, 7, 8, 8, 9, 10, 10, 11, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 13, 7, 8, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 7 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Hajnal, A. and Lovasz, L. "An Algorithm to Prevent the Propagation of Certain Diseases at Minimum Cost." Section 10.1 in Interfaces Between Computer Science and Operations Research: Proceedings of a Symposium Held at the Mathematisch Centrum, Amsterdam, September 7-10, 1976 (Ed. J. K. Lenstra, A. H. G. Rinnooy Kan and P. van Emde Boas). Amsterdam: Matematisch Centrum, 1978.

Vardi, I. "The Condom Problem." Ch. 10 in Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, pp. 203-222, 1991.

LINKS

Nathaniel Johnston, Rows n=1..150, flattened

Eric W. Weisstein, Glove Problem.

Ilan Vardi, The condom problem

FORMULA

a(m,n) = 2 when m = n = 2. a(m,n) = (m+1)/2 when n = 1 and m is odd. a(m,n) = ceiling((m/2) + (2*n/3)) otherwise.

EXAMPLE

The triangle begins:

1

2 2

2 3 4

3 4 4 5

3 4 5 6 6

4 5 5 6 7 7

4 5 6 7 7 8 9

...

MAPLE

A155940 := proc(m, n) if(n=2 and m=2)then return 2: elif(n=1 and m mod 2 = 1)then return (m+1)/2: else return ceil((m/2) + (2*n/3)): fi: end: for m from 1 to 7 do seq(A155940(m, n), n=1..m); od; # Nathaniel Johnston, May 03 2011

MATHEMATICA

vos[{m_, n_}]:=Which[m==n==2, 2, n==1&&OddQ[m], (m+1)/2, True, Ceiling[ m/2+2 n/3]]; Flatten[Table[vos[{m, n}], {m, 20}, {n, m}]] (* Harvey P. Dale, Jun 10 2013 *)

CROSSREFS

Sequence in context: A241504 A342247 A016729 * A186963 A060473 A055034

Adjacent sequences:  A155937 A155938 A155939 * A155941 A155942 A155943

KEYWORD

easy,nonn,tabl

AUTHOR

Jonathan Vos Post, Jan 31 2009

EXTENSIONS

Edited by Nathaniel Johnston, May 03 2011

STATUS

approved

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Last modified March 9 03:05 EST 2021. Contains 341961 sequences. (Running on oeis4.)