|
Search: id:A051336
|
|
|
| A051336 |
|
Number of arithmetic progressions in {1,2,3,...,n}, including trivial arithmetic progressions of lengths 1 and 2. |
|
+0
4
|
|
| 1, 3, 7, 13, 22, 33, 48, 65, 86, 110, 138, 168, 204, 242, 284, 330, 381, 434, 493, 554, 621, 692, 767, 844, 929, 1017, 1109, 1205, 1307, 1411, 1523, 1637, 1757, 1881, 2009, 2141, 2282, 2425, 2572, 2723, 2882, 3043, 3212, 3383, 3560, 3743, 3930, 4119
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..1000
|
|
FORMULA
|
Theorem: the second differences give tau(n+1), the number of divisors of n+1 (A000005).
The number of arithmetic subsequences of [1, ..., n] with successive-term increment i and length k is (n-i*(k-1))(i > 0, k > 0, n > i*(k-1)). - Robert E. Sawyer (rs.1(AT)mindspring.com)
a(n) = n + sum { i=1..n-1, j=1..floor(n/i) } (n - i*j) - Robert E. Sawyer (rs.1(AT)mindspring.com)
|
|
EXAMPLE
|
a(1): [1]; a(2): [1],[2],[1,2]; a(3): [1],[2],[3],[1,2],[1,3],[2,3],[1,2,3]
|
|
CROSSREFS
|
a(n) = n + A078567(n).
Cf. A000005, A054519.
Sequence in context: A155354 A136219 A078582 this_sequence A002623 A081662 A091652
Adjacent sequences: A051333 A051334 A051335 this_sequence A051337 A051338 A051339
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
John W. Layman (layman(AT)math.vt.edu), Nov 02 1999
|
|
|
Search completed in 0.002 seconds
|
