|
%I #12 Oct 11 2015 10:52:13
%S 7,8,5,13,4,3,19,11,1,1,20,17,9,0,0,24,14,15,6,0,0,25,16,10,11,2,0,0,
%T 28,22,11,6,9,0,0,0,33,22,18,9,2,6,0,0,0,36,29,18,12,6,0,2,0,0,0,37,
%U 27,27,12,6,2,0,0,0,0,0,40,35,23,23,6,2,0,0,0,0,0,0,43,32,31,21,21,2,0,0,0,0,0,0,0,49,41,26,29,17,17,0,0,0,0,0,0,0,0,50,46,39,22,27,15,15,0,0,0,0,0,0,0,0
%N Square array A(row,col) read by antidiagonals: A(1,col) = A045765(col); for row > 1, if A(row-1,col) = 0 then A(row,col) = 0, otherwise A(row,col) = A049820(A(row-1,col)).
%C The array is read by downwards antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
%C Column n gives the trajectory of iterates of A049820, when starting from A045765(n), thus stepping through successive parent-nodes when starting from the n-th leaf in the tree generated by edge-relation A049820(child) = parent, until finally reaching the fixed point 0, which is the root of the whole tree.
%C A portion of the hanging tail of each column (upward from the first encountered zero) converges towards A259934, although not in monotone fashion.
%H Antti Karttunen, <a href="/A262898/b262898.txt">Table of n, a(n) for n = 1..5050; the first 100 antidiagonals of the array</a>
%F A(1,col) = A045765(col), and for row > 1, if A(row-1,col) = 0 then A(row,col) = 0, otherwise A(row,col) = A049820(A(row-1,col)).
%e The top left corner of the array:
%e 7, 8, 13, 19, 20, 24, 25, 28, 33, 36, 37, 40, 43, 49, 50, 52, 55, 56
%e 5, 4, 11, 17, 14, 16, 22, 22, 29, 27, 35, 32, 41, 46, 44, 46, 51, 48
%e 3, 1, 9, 15, 10, 11, 18, 18, 27, 23, 31, 26, 39, 42, 38, 42, 47, 38
%e 1, 0, 6, 11, 6, 9, 12, 12, 23, 21, 29, 22, 35, 34, 34, 34, 45, 34
%e 0, 0, 2, 9, 2, 6, 6, 6, 21, 17, 27, 18, 31, 30, 30, 30, 39, 30
%e 0, 0, 0, 6, 0, 2, 2, 2, 17, 15, 23, 12, 29, 22, 22, 22, 35, 22
%e 0, 0, 0, 2, 0, 0, 0, 0, 15, 11, 21, 6, 27, 18, 18, 18, 31, 18
%e 0, 0, 0, 0, 0, 0, 0, 0, 11, 9, 17, 2, 23, 12, 12, 12, 29, 12
%e 0, 0, 0, 0, 0, 0, 0, 0, 9, 6, 15, 0, 21, 6, 6, 6, 27, 6
%e 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 11, 0, 17, 2, 2, 2, 23, 2
%e 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 9, 0, 15, 0, 0, 0, 21, 0
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 11, 0, 0, 0, 17, 0
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 9, 0, 0, 0, 15, 0
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 11, 0
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 9, 0
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0
%e ...
%o (Scheme)
%o (define (A262898 n) (A262898bi (A002260 n) (A004736 n)))
%o (define (A262898bi row col) (if (= 1 row) (A045765 col) (if (zero? (A262898bi (- row 1) col)) 0 (A049820 (A262898bi (- row 1) col)))))
%Y Transpose: A262899.
%Y Cf. A045765 (row 1), A262902 (row 2).
%Y Cf. A049820, A259934.
%Y Cf. also A257264.
%K nonn,tabl
%O 1,1
%A _Antti Karttunen_, Oct 06 2015
|
