A265236 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.

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, 40, 38, 34, 49, 40, 38, 9, 34, 30, 29, 31, 31, 31, 38, 34, 47, 39, 28, 34, 53, 40, 46, 38, 66, 55, 54, 48, 59, 46, 46, 48, 75, 62, 58, 52, 67, 58, 48, 11, 43, 38

Offset

0,3

Comments

A, B and C are allowed to be zero, in contrast to A265008;

a(A000225(n)) = A265008(A000225(n));

a(A062289(n)) != A265008(A062289(n)).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

For n > 0: a(n) = A265008(n) + A043545(n) * (2*A078822(n) - 1).

Example

.  n | A007088 | A119709     |  a |
. ---+---------+-------------+----+-------------------------------------
.  2 |      10 | [0,1,2]     |  8 = #{(0,0,0), (0,1,0), (0,2,0), (1,0,0),
.    |         |             |        (2,0,0), (1,1,1), (1,2,2), (2,1,2)}
.  3 |      11 | [1,3]       |  3 = #{(1,1,1), (1,3,3), (3,1,3)}
.  4 |     100 | [0,1,2,4]   | 13 = #{(0,0,0), (0,1,0), (0,2,0), (0,4,0),
.    |         |             |         (1,0,0), (2,0,0), (4,0,0), (1,1,1),
.    |         |             |         (1,2,2), (2,1,2), (1,4,4), (2,2,4),
.    |         |             |         (4,1,4)}
.  5 |     101 | [0,1,2,5]   | 12 = #{(0,0,0), (0,1,0), (0,2,0), (0,5,0),
.    |         |             |         (1,0,0), (2,0,0), (5,0,0), (1,1,1),
.    |         |             |         (1,2,2), (2,1,2), (1,5,5), (5,1,5)}
.  6 |     110 | [0,1,2,3,6] | 18 = #{(0,0,0), (0,1,0), (0,2,0), (0,3,0),
.    |         |             |         (0,6,0), (1,0,0), (2,0,0), (3,0,0),
.    |         |             |         (6,0,0), (1,1,1), (1,2,2), (2,1,2),
.    |         |             |         (1,3,3), (3,1,3), (1,6,6), (2,3,6),
.    |         |             |         (3,2,6), (6,1,6)}
.  7 |     111 | [1,3,7]     |≈ 5 = #{(1,1,1), (1,3,3), (3,1,3), (1,7,7),
.    |         |             |         (7,1,7)} .

Prog

(Haskell)
a265236 n = length [() | let cs = a119709_row n, a <- cs, b <- cs, c <- cs,
                         a * b == c || c == 0 && a * b == 0]

Crossrefs

Cf. A007088, A119709, A265008, A265183 (decimal case), A000225, A062289, A043545, A078822.

Sequence in context: A069200 A069218 A248295 * A286568 A070608 A070486

Adjacent sequences: A265233 A265234 A265235 * A265237 A265238 A265239

Keyword

nonn

Author

Reinhard Zumkeller, Dec 06 2015

Extensions

Suggested by N. J. A. Sloane.

Status

approved