%I A036561
%S A036561 1,2,3,4,6,9,8,12,18,27,16,24,36,54,81,32,48,72,108,162,243,64,96,144,
%T A036561 216,324,486,729,128,192,288,432,648,972,1458,2187,256,384,576,864,
%U A036561 1296,1944,2916,4374,6561,512,768,1152,1728,2592,3888,5832,8748,13122
%N A036561 Triangle of numbers in which i-th row is {2^(i-j)*3^j, 0<=j<=i}; i >= 
               0.
%C A036561 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
%C A036561 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
%C A036561 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
%D A036561 Jay Kappraff, "Beyond Measure", World Scientific, 2002, p. 148.
%H A036561 Robert Sedgewick, <a href="http://www.cs.princeton.edu/~rs/talks/shellsort.ps">
               Analysis of shellsort and related algorithms</a>, Fourth European 
               Symposium on Algorithms, Barcelona, September, 1996.
%e A036561 1
%e A036561 2 3
%e A036561 4 6 9
%e A036561 8 12 18 27
%e A036561 16 24 36 54 81
%e A036561 32 48 72 108 162 243
%t A036561 Table[ 2^(i-j) 3^j, {i, 0, 12}, {j, 0, i} ]
%Y A036561 Cf. A003586, A000079, A000244, A007283, A025197, A005010, A003946, A005051.
%Y A036561 Sequence in context: A035312 A056230 A119919 this_sequence A082976 A047419 
               A135205
%Y A036561 Adjacent sequences: A036558 A036559 A036560 this_sequence A036562 A036563 
               A036564
%K A036561 nonn,easy,tabl,nice
%O A036561 0,2
%A A036561 N. J. A. Sloane (njas(AT)research.att.com).
%E A036561 More terms from W. Meeussen (wouter.meeussen(AT)pandora.be)