login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A108235 Number of partitions of {1,2,...,3n} into n triples (X,Y,Z) each satisfying X+Y=Z. 9
1, 1, 0, 0, 8, 21, 0, 0, 3040, 20505, 0, 0, 10567748, 103372655, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(0)=1 by convention.

REFERENCES

M. Beck and T. Zaslavsky, Six little squares and how their numbers grow, J. Integer Sequences, 13 (2010), #10.6.2.

LINKS

Table of n, a(n) for n=0..15.

R. J. Nowakowski, Generalizations of the Langford-Skolem problem, M.S. Thesis, Dept. Math., Univ. Calgary, May 1975. [Scanned copy, with permission.]

Wikipedia, Dancing Links

FORMULA

a(n) = 0 unless n == 0 or 1 (mod 4). For n == 0 or 1 (mod 4), a(n) = A002849(3n). See A002849 for references and further information.

EXAMPLE

For m = 1 the unique solution is 1 + 2 = 3.

For m = 4 there are 8 solutions:

1.5..6.|.1.5..6..|.2..5..7.|.1..6..7

2.8.10.|.3.7.10..|.3..6..9.|.4..5..9

4.7.11.|.2.9.11..|.1.10.11.|.3..8.11

3.9.12.|.4.8.12..|.4..8.12.|.2.10.12

------------------------------------

2.4..6.|.2..6..8.|.3..4..7.|.3..5..8

1.9.10.|.4..5..9.|.1..8..9.|.2..7..9

3.8.11.|.3..7.10.|.5..6.11.|.4..6.10

5.7.12.|.1.11.12.|.2.10.12.|.1.11.12

PROG

(Sage) A = lambda n:sum(1 for t in DLXCPP([(a-1, b-1, a+b-1) for a in (1..3*n) for b in (1..min(3*n-a, a-1))])) # Tomas Boothby, Oct 11 2013

CROSSREFS

Cf. A002848, A002849, A161826, A202951, A202952.

Sequence in context: A221067 A217018 A079386 * A130021 A003864 A182602

Adjacent sequences:  A108232 A108233 A108234 * A108236 A108237 A108238

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Feb 10 2010, based on posting to the Sequence Fans Mailing List by Franklin T. Adams-Watters, Richard K. Guy, R. H. Hardin, Alois P. Heinz, Andrew Weimholt and others.

EXTENSIONS

a(12) from R. H. Hardin, Feb 11 2010

a(12) confirmed and a(13) computed (using Knuth's dancing links algorithm) by Alois P. Heinz, Feb 11 2010

a(13) confirmed by Tomas Boothby, Oct 11 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 17 15:19 EDT 2017. Contains 290635 sequences.