%I #16 Aug 19 2018 03:52:50
%S 1,2,3,4,6,8,5,11,17,22,7,14,28,45,55,9,19,37,70,112,137,10,23,48,93,
%T 171,276,334,12,26,57,118,228,417,671,812,13,31,66,141,287,556,1010,
%U 1627,1965,15,34,77,164,344,697,1347,2444,3934,4751,16,39
%N Joint-rank array of numbers j*r^(i-1), where r=1+sqrt(2), read by antidiagonals.
%C Joint-rank arrays are defined in the first comment at A182801. (row 1)=A087063. First 3 columns are A020062, A020063, A020064.
%C Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
%H G. C. Greubel, <a href="/A182831/b182831.txt">Rows n=1..100 of triangle, flattened</a>
%F T(i,j) = Sum_{n>=1} floor(j*(1+sqrt(2))^(i-n))).
%e Northwest corner:
%e 1 2 4 5 ...
%e 3 6 11 14 ...
%e 8 17 28 37 ...
%e 22 45 70 93 ...
%e ...
%t T[n_, k_] := Sum[Floor[k*(1 + Sqrt[2])^(n - j)], {j, 1, 100}]; Table[T[k + 1, n - k], {n,1,10}, {k, 0, n-1}]//Flatten (* _G. C. Greubel_, Aug 18 2018 *)
%Y Cf. A182801.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Dec 07 2010