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%I #7 Jun 12 2021 23:36:22
%S 0,1,1,2,3,2,3,5,7,3,4,8,12,8,4,5,10,21,13,17,5,6,13,26,22,31,18,6,7,
%T 15,35,27,58,32,20,7,8,18,40,36,73,59,34,21,8,9,22,49,41,100,74,62,35,
%U 22,9,10,24,63,50,115,101,76,63,36,45,10,11,27,68,64,142,116,104,77,64,87,46
%N Array A(x,y): Position of the totally balanced binary string obtained by concatenating the binary strings A014486(x) & A014486(y) in such a way that the latter is inserted after the least significant 1-bit of the former, followed by the remaining 0-bits, if any. Listed antidiagonalwise as A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), ...
%C This table is induced by the list-function 'app-to-xrt' whose Scheme-definition is given below, in the same way as A085201 is induced by the ordinary 'append'-function.
%F a(0, y) = y, a(x, y) = A057548(a(A072771(x), y)) if A072772(x)=0, otherwise A072764bi(A072771(x), a(A072772(x), y)).
%F a(x, y) = A080300(A085211bi(A014486(x), A014486(y))) = A085200(A085219bi(A071155(y), A071155(x))).
%o (MIT Scheme) (define (A085203bi x y) (A080300 (A085211bi (A014486 x) (A014486 y))))
%o (define (A085203 n) (A085203bi (A025581 n) (A002262 n)))
%o (define (A085204 n) (A085203bi (A002262 n) (A025581 n)))
%o (HERE IS THE CORRESPONDING FUNCTION FOR S-EXPRESSIONS): (define (app-to-xrt a b) (cond ((null? a) b) ((pair? (cdr a)) (cons (car a) (app-to-xrt (cdr a) b))) (else (cons (app-to-xrt (car a) b) (cdr a)))))
%o (AND THE DESTRUCTIVE VARIANT): (define (app-to-xrt! a b) (cond ((null? a) b) (else (let recurse ((a a) (b b)) (cond ((and (not (pair? (car a))) (not (pair? (cdr a)))) (set-car! a b)) ((pair? (cdr a)) (recurse (cdr a) b)) (else (recurse (car a) b)))) a)))
%Y Transpose: A085204. Variant: A085201. Row 1: A085225, Column 1: A057548.
%Y Cf. also A014486, A080300, A025581, A002262.
%K nonn,tabl
%O 0,4
%A _Antti Karttunen_ Jun 23 2003
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