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Joint-rank array of the numbers j*(1+tau)^2*(i-1), where tau = golden ratio = (1+sqrt(5))/2, i>=1, read by antidiagonals.
2

%I #10 Mar 30 2012 18:57:12

%S 1,2,3,4,7,9,5,11,20,26,6,15,31,55,72,8,19,42,84,148,194,10,23,53,113,

%T 224,393,515,12,28,64,142,300,592,1036,1357,13,32,75,171,376,791,1557,

%U 2721,3563,14,36,86,200,452,990,2078,4085,7134,9340

%N Joint-rank array of the numbers j*(1+tau)^2*(i-1), where tau = golden ratio = (1+sqrt(5))/2, i>=1, read by antidiagonals.

%C Joint-rank arrays are defined in the first comment at A182801. There r=tau; here r=1+tau=(tau)^2.

%C (Column 1)=A054963. Every positive integer occurs exactly once, so that as a sequence, A182802 is a permutation of the positive integers.

%F T(i,j)=SUM{floor(j*(tau)^(2*(i-n))): n>=1}.

%e Northwest corner:

%e 1....2....4....5....6...

%e 3....7...11...15...19...

%e 9...20...31...42...53...

%e 26..55...84..113..142...

%Y Cf. A182801.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Dec 05 2010