A130808 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A130808

Magic side-sum constants of magic triangles of Yates using the numbers 1 to 9.

17, 19, 20, 21, 23

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A magic triangle of Yates, with nine numbers a,b,c,d,e,f,g,h,i has the form

d f

e g

b h i c

The corner sum C = a+b+c and magic side-sum S = a+d+e+b = b+h+i+c = a+f+g+c are related by C=3*(S - 15). Since here, 1+2+3 <= C <= 7+8+9, we have 17 <= S <= 23. Finally, an argument based on a contradiction proof eliminates the values of 18 and 22 for S.

REFERENCES

U. Nagamani, "The magic triangles of Yates" in 'Science Reporter', pp. 65-66, Jan. 1978, Vol. 15, No. 1, CSIR, New Delhi.

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

All the magic triangles are illustrated:

1 1 4 3 7

9 6 8 9 8 1 8 7 3 6

5 7 6 2 3 9 4 2 5 1

2 8 4 3 4 5 3 7 5 7 2 6 6 5 1 9 8 2 4 9

CROSSREFS

Sequence in context: A041610 A042399 A156656 * A194389 A030127 A115849

Adjacent sequences: A130805 A130806 A130807 * A130809 A130810 A130811

KEYWORD

fini,full,nonn

AUTHOR

Lekraj Beedassy, Aug 20 2007

STATUS

approved