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%I #7 Dec 06 2015 10:31:00
%S 1,1,8,3,13,12,18,5,19,17,18,20,31,26,28,7,26,23,23,26,31,22,32,28,47,
%T 40,38,34,49,40,38,9,34,30,29,31,31,31,38,34,47,39,28,34,53,40,46,38,
%U 66,55,54,48,59,46,46,48,75,62,58,52,67,58,48,11,43,38
%N Number of solutions to the equation A x B = C, where A, B and C are nonnegative numbers appearing as (contiguous) substrings of the binary representation of n.
%C A, B and C are allowed to be zero, in contrast to A265008;
%C a(A000225(n)) = A265008(A000225(n));
%C a(A062289(n)) != A265008(A062289(n)).
%H Reinhard Zumkeller, <a href="/A265236/b265236.txt">Table of n, a(n) for n = 0..10000</a>
%F For n > 0: a(n) = A265008(n) + A043545(n) * (2*A078822(n) - 1).
%e . n | A007088 | A119709 | a |
%e . ---+---------+-------------+----+-------------------------------------
%e . 2 | 10 | [0,1,2] | 8 = #{(0,0,0), (0,1,0), (0,2,0), (1,0,0),
%e . | | | (2,0,0), (1,1,1), (1,2,2), (2,1,2)}
%e . 3 | 11 | [1,3] | 3 = #{(1,1,1), (1,3,3), (3,1,3)}
%e . 4 | 100 | [0,1,2,4] | 13 = #{(0,0,0), (0,1,0), (0,2,0), (0,4,0),
%e . | | | (1,0,0), (2,0,0), (4,0,0), (1,1,1),
%e . | | | (1,2,2), (2,1,2), (1,4,4), (2,2,4),
%e . | | | (4,1,4)}
%e . 5 | 101 | [0,1,2,5] | 12 = #{(0,0,0), (0,1,0), (0,2,0), (0,5,0),
%e . | | | (1,0,0), (2,0,0), (5,0,0), (1,1,1),
%e . | | | (1,2,2), (2,1,2), (1,5,5), (5,1,5)}
%e . 6 | 110 | [0,1,2,3,6] | 18 = #{(0,0,0), (0,1,0), (0,2,0), (0,3,0),
%e . | | | (0,6,0), (1,0,0), (2,0,0), (3,0,0),
%e . | | | (6,0,0), (1,1,1), (1,2,2), (2,1,2),
%e . | | | (1,3,3), (3,1,3), (1,6,6), (2,3,6),
%e . | | | (3,2,6), (6,1,6)}
%e . 7 | 111 | [1,3,7] |≈ 5 = #{(1,1,1), (1,3,3), (3,1,3), (1,7,7),
%e . | | | (7,1,7)} .
%o (Haskell)
%o a265236 n = length [() | let cs = a119709_row n, a <- cs, b <- cs, c <- cs,
%o a * b == c || c == 0 && a * b == 0]
%Y Cf. A007088, A119709, A265008, A265183 (decimal case), A000225, A062289, A043545, A078822.
%K nonn
%O 0,3
%A _Reinhard Zumkeller_, Dec 06 2015
%E Suggested by _N. J. A. Sloane_.
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