|
Search: id:A126683
|
|
|
| A126683 |
|
a(n) is the number of partitions of the n-th triangular number n(n+1)/2 into distinct odd parts. |
|
+0
1
|
|
| 1, 1, 1, 2, 4, 8, 16, 33, 68, 144, 312, 686, 1523, 3405, 7652, 17284, 39246, 89552, 205253, 472297, 1090544, 2525904, 5867037, 13663248, 31896309, 74628130, 174972341, 411032475, 967307190, 2280248312, 5383723722, 12729879673
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
Also the number of self-conjugate partitions of the n-th triangular number.
|
|
EXAMPLE
|
The 5th triangular number is 15. Writing this as a sum of distinct odd numbers: 15 = 11 + 3 + 1 = 9 + 5 + 1 = 7 + 5 + 3 are all the possibilities. So a(5) = 4.
|
|
MAPLE
|
g:=product(1+x^(2*j+1), j=0..900): seq(coeff(g, x, n*(n+1)/2), n=1..40); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007
|
|
CROSSREFS
|
Sequences A066655 and A104383 do the same thing for triangular numbers, with partitions or distinct partitions. Sequences A072213 and A072243 are analogues for squares rather than triangular numbers.
Adjacent sequences: A126680 A126681 A126682 this_sequence A126684 A126685 A126686
Sequence in context: A119610 A121485 A098588 this_sequence A005821 A004149 A129986
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Moshe Newman (mshnoiman(AT)hotmail.com), Feb 15 2007
|
|
EXTENSIONS
|
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007
|
|
|
Search completed in 0.002 seconds
|
