0,2

The triangle pertaining to this sequence has the property that every row, every column and every diagonal contains a nontrivial geometric progression. More interestingly every line joining any two elements contains a nontrivial geometric progression. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jan 02 2002

Kappraff states (p. 148-149): "I shall refer to this as Nicomachus' table since an identical table of numbers appeared in the Arithmetic of Nicomachus of Gerasa (circa 150 A.D.)" The table was rediscovered during the Italian Renaissance by Leon Battista Alberti, who incorporated the numbers in dimensions of his buildings and in a system of musical proportions. Kappraff states "Therefore a room could exhibit a 4:6 or 6:9 ratio but not 4:9. This insured that ratios of these lengths would embody musical ratios". - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 18 2003

Row sums give A001047; central terms give A000400; T(n,k)=A013620(n,k)/A007318(n,k). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 14 2006

Jay Kappraff, "Beyond Measure", World Scientific, 2002, p. 148.

Robert Sedgewick, Analysis of shellsort and related algorithms, Fourth European Symposium on Algorithms, Barcelona, September, 1996.

1

2 3

4 6 9

8 12 18 27

16 24 36 54 81

32 48 72 108 162 243

Table[ 2^(i-j) 3^j, {i, 0, 12}, {j, 0, i} ]

Cf. A003586, A000079, A000244, A007283, A025197, A005010, A003946, A005051.

Sequence in context: A035312 A056230 A119919 this_sequence A082976 A047419 A135205

Adjacent sequences: A036558 A036559 A036560 this_sequence A036562 A036563 A036564

nonn,easy,tabl,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from W. Meeussen (wouter.meeussen(AT)pandora.be)