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%I #12 Feb 03 2015 16:10:16
%S 1,2,1,1,1,3,2,6,12,4,4,9,1,9,21,5,3,13,48,102,31,3,7,30,75,36,10,183,
%T 2,15,39,6,112,426,912,274,7,18,22,58,264,669,160,684,1641,8,10,7,129,
%U 345,198,1003,3828,8202,2461,1,6,57,156,193,517,2370,6015,2871,3076,14763,5,24,66,85,117,1155,3099,889,9022,34446,73812,22144
%N Square array: A(row,col) = A003602(A254051(row,col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
%C Starting with an odd number x = A135765(row,col), the result after one combined Collatz step (3x+1)/2 is found in A254051(row+1,col), and after iterated [i.e., we divide all powers of 2 out] Collatz step: x_new <- A139391(x) = A000265(3x+1) the resulting odd number x_new is located A135764(1,A(row+1,col)).
%C What the resulting odd number will be, is given by A254101(row+1,col).
%H Antti Karttunen, <a href="/A254055/b254055.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array</a>
%e The top left corner of the array:
%e 1, 2, 1, 2, 4, 5, 3, 2, 7, 8, 1, ...
%e 1, 1, 6, 9, 3, 7, 15, 18, 10, 6, 24, ...
%e 3, 12, 1, 13, 30, 39, 22, 7, 57, 66, 18, ...
%e 4, 9, 48, 75, 6, 58, 129, 156, 85, 25, 210, ...
%e 21, 102, 36, 112, 264, 345, 193, 117, 507, 588, 79, ...
%e 31, 10, 426, 669, 198, 517, 1155, 1398, 760, 441, 1884, ...
%e 183, 912, 160, 1003, 2370, 3099, 1732, 66, 4557, 5286, 1413, ...
%e 274, 684, 3828, 6015, 889, 4648, 10389, 12576, 6835, 496, 16950, ...
%e etc.
%o (Scheme, two versions)
%o (define (A254055 n) (A254055bi (A002260 n) (A004736 n)))
%o (define (A254055bi row col) (A003602 (A254051bi row col))) ;; A254051bi given in A254051.
%o (define (A254055v2 n) (A254055biv2 (A002260 n) (A004736 n)))
%o (define (A254055biv2 row col) (A003602 (A048673 (A135764bi row (A249745 col))))) ;; A135764bi given in A135764.
%Y Cf. A003602, A002260, A004736.
%Y Related arrays: A135764, A135765, A254051, A254101, A254102.
%K nonn,tabl
%O 1,2
%A _Antti Karttunen_, Jan 27 2015
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