------ Original Message ------ Received: Thu, 30 Jun 2005 05:57:43 PM PDT From: Richard Schroeppel <rcs@CS.Arizona.EDU> To: math-fun@mailman.xmission.com Subject: [math-fun] programming orbits, unequal partitions ...
--- RWG: Can your matrices of Q-products explain why Unequal-Partitions(N) has so many powers of 2 divisors? The most egregious values (from A&S table 24.5 on page 836) are Q(20) = 64, Q(34) = 512, Q(45) = 2048.
I don't find any other powers of 2 up to 2^33 (besides 1,2,4,8,32) so it could be a small number thing. Note that Q(51)=4097 though.
There are occasional odd Q(N), but no apparent pattern.
The odd Q occur at the values of A001318 ID Number: A001318 (Formerly M1336 and N0511) URL: http://www.research.att.com/projects/OEIS?Anum=A001318 Sequence: 0,1,2,5,7,12,15,22,26,35,40,51,57,70,77,92,100,117,126,145, 155,176,187,210,222,247,260,287,301,330,345,376,392,425,442, 477,495,532,551,590,610,651,672,715,737,782,805,852,876,925, 950,1001,1027,1080,1107,1162,1190,1247,1276,1335 Name: Generalized pentagonal numbers: n(3n-1)/2, n=0, +- 1, +- 2,....
Rich rcs@cs.arizona.edu