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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
A. Hajnal and L. Lovasz, "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.
I. Vardi, "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
Ilan Vardi, The condom problem
Eric Weisstein's World of Mathematics, Glove 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
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 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)