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Help deriving integer sequence formula 
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#1
Jan1610, 03:51 PM

P: 145

Hi
I'm playing around with partitions and have come up with an integer sequence representing the maximum number of partitions of various "widths" that display the following properties:  min values in partition are equal  max values in partition are equal  partitions contain equal number of members  sum of members is equal For example, given: min = 1 max = 6 count = 4 sum = 14 There are only two partitions that satisfy the constraints {1,3,4,6} {1,2,5,6} Using a brute force algorithm, I came up with the following maximums for width = {1, 2, 3, 4 ..., 24} 1, 1, 1, 1, 1, 2, 2, 3, 5, 8, 12, 20, 32, 58, 94, 169, 289, 526, 910, 1667, 2934, 5448, 9686, 18084 My algorithm breaks at 25 due to the huge memory trequirements needed to sample every possible combination. I plugged it into Sloan's, but no luck. With a little tweaking, the series seems like it might have some sort of partial relationship with the Fibonacci and Lucas series, but I haven't been able to come up with anything concrete.
Thanks for any help 


#2
Jan2410, 08:28 PM

P: 894




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