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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 08:38 EDT 2020. Contains 337268 sequences. (Running on oeis4.)