|
%I #8 Apr 27 2017 11:38:52
%S 6,27,11,220,92,28,1765,741,229,37,14126,5934,1838,302,46,113015,
%T 47479,14711,2423,375,55,1808248,759672,235384,38776,6008,888,120,
%U 28931977,12154761,3766153,620425,96137,14217,1929,137,462911642,194476186,60258458,9926810,1538202,227482,30874,2202,154
%N Square array A(m,n) = number whose binary expansion is the concatenation of those of { m, m+1, ..., m+n }, with m, n >= 1, read by falling antidiagonals.
%C A column n = 0 would have A(m,0) = m. A row m = 0 would have A(0,n) = A(1,n-1) for all n > 0.
%e A(1,1) = 6 = 110[2], concatenation of 1 & 2 written in binary.
%e A(1,2) = 27 = 110101[2], concatenation of 1 & 2 & 3 written in binary.
%e A(2,1) = 11 = 1011[2], concatenation of 2 & 3 written in binary.
%e The table starts:
%e 6 27 220 1765 14126 113015 1808248 28931977 462911642
%e 11 92 741 5934 47479 759672 12154761 194476186 3111618987
%e 28 229 1838 14711 235384 3766153 60258458 964135339 15426165436
%e 37 302 2423 38776 620425 9926810 158828971 2541263548 40660216781
%e 46 375 6008 96137 1538202 24611243 393779900 6300478413 100807654622
%e 55 888 14217 227482 3639723 58235580 931769293 14908308702 238532939247
%e 120 1929 30874 493995 7903932 126462925 2023406814 32374509039 1035984289264
%e 137 2202 35243 563900 9022413 144358622 2309737967 73911614960 2365171678737
%e 154 2475 39612 633805 10140894 162254319 5192138224 166148423185 5316749541938
%o (PARI) a(m,n)={for(i=m+1,m+n,m=m<<#binary(i)+i);m}
%Y Cf. A285807 for the base-10 variant.
%K nonn,base,tabl
%O 1,1
%A _M. F. Hasler_, Apr 27 2017
|
