|
Search: id:A000630
|
|
|
| A000630 |
|
Number of ways to represent n using the binary operator a * b = 2^a + b. |
|
+0
1
|
|
| 1, 1, 2, 3, 7, 12, 23, 41, 81, 149, 282, 522, 987, 1843, 3463, 6473, 12160, 22773, 42719, 80025, 150074, 281258, 527320, 988334, 1852849, 3473061, 6510681, 12204139, 22877649, 42884585, 80389797, 150692973, 282481747, 529522496, 992614937
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
D. E. Knuth, personal communication.
|
|
FORMULA
|
Sum a(n) q^n = (1 - Sum a(n) q^(2^n ) )^-1.
As n increases, a(n+1)/a(n) approaches a value x = 1.874542... satisfying 1 = ( Sum a(j)/x^(2^j), j >= 0 ) [ David W. Wilson ].
|
|
EXAMPLE
|
E.g. 4=1+1+1+1=2^1 + 1+1=2^1 +2^1 =2^2 = 2^1+1 =1+2^1 + 1=1+1+2^1.
|
|
CROSSREFS
|
Sequence in context: A056179 A027675 A054176 this_sequence A036538 A108742 A018240
Adjacent sequences: A000627 A000628 A000629 this_sequence A000631 A000632 A000633
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from David W. Wilson (davidwwilson(AT)comcast.net)
|
|
|
Search completed in 0.002 seconds
|
