|
Search: id:A000929
|
|
|
| A000929 |
|
Dimension of n-th degree part of Steenrod algebra. |
|
+0
7
|
|
| 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 20, 22, 23, 26, 28, 29, 32, 35, 37, 41, 45, 47, 51, 55, 58, 63, 68, 72, 77, 82, 86, 92, 98, 103, 111, 118, 123, 131, 139, 145, 154, 164, 171, 180, 190, 198, 208, 219, 229, 241, 253, 264, 278, 291
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Number of partitions of n into parts of the form 2^j-1, j=1,2,... (called s-partitions). Example: a(7)=4 because we have [7], [3,3,1], [3,1,1,1,1] and [1,1,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 2006
|
|
REFERENCES
|
P. C. P. Bhatt, An interesting way to partition a number, Inform. Process. Lett., 71, 1999, 141-148.
W. M. Y. Goh, P. Hitczenko and A. Shokoufandeh, s-partitions, Inform. Process. Lett., 82, 2002, 327-329.
Steenrod, N. and Epstein, D., "Cohomology Operations," Princeton Univ. Press, 1962.
|
|
LINKS
|
R. Zumkeller, Table of n, a(n) for n = 0..512 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 18 2009]
|
|
FORMULA
|
n-th term is number of ways to write n as a sum a_1 + ... + a_k where the a_i are positive integers and a_i >= 2 * a_{i-1}.
1/product( (1-x^(2^i-1)),i=0..infinity) (Simon Plouffe).
a(n) = p(n,1) with p(n,k) = if k<=n then p(n-k,k)+p(n,2*k+1) else 0^n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 18 2009]
|
|
MAPLE
|
The sequence is C(n, n) where C := proc(m, n) option remember; local k, a; if m = 0 then if n = 0 then 1 else 0 fi; elif m > n then C(n, n); else a := 0; for k from 0 to m do a := a + C(floor(k/2), n-k) od; a; fi end;
g:=1/product(1-x^(2^k-1), k=1..10): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..64); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 2006
|
|
CROSSREFS
|
Cf. A117145.
A000225, A000041, A018819, A079559. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 18 2009]
Sequence in context: A070547 A094838 A025768 this_sequence A029146 A029053 A053254
Adjacent sequences: A000926 A000927 A000928 this_sequence A000930 A000931 A000932
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Dan Christensen [ jdchrist(AT)math.mit.edu ]
|
|
|
Search completed in 0.002 seconds
|
