[seqfan] Permutations constructable from consecutive sums

[Ron Hardin]

(The presence of 0 makes constructed permutations and the non-negative integer 
list one-to-one)

1,2,4,12,44,176,768,4000,22896,142336,967040,7258368,57919872,490253312,
4455645952,43468799232
Number of permutations of 0..(n-1) representable as consecutive sums of 2 
adjacent elements of a sequence of n+1 non-negative integers

1,2,4,8,18,56,206,866,3662,16304,77448,405594,2296514,13989280,89990314,
612195224
Number of permutations of 0..(n-1) representable as consecutive sums of 3 
adjacent elements of a sequence of n+2 non-negative integers

1,2,4,8,16,34,82,252,890,3644,15390,67646,301210,1397898,6786792,
35154332
Number of permutations of 0..(n-1) representable as consecutive sums of 4 
adjacent elements of a sequence of n+3 non-negative integers

1,2,4,8,16,32,66,148,376,1138,3834,14832,60584,263480,1159034,5218514
Number of permutations of 0..(n-1) representable as consecutive sums of 5 
adjacent elements of a sequence of n+4 non-negative integers

1,2,4,8,16,32,64,130,278,654,1728,5196,16948,61518,238060,999268
Number of permutations of 0..(n-1) representable as consecutive sums of 6 
adjacent elements of a sequence of n+5 non-negative integers

1,2,4,8,16,32,64,128,258,536,1190,2918,7954,23914
Number of permutations of 0..(n-1) representable as consecutive sums of 7 
adjacent elements of a sequence of n+6 non-negative integers

1,2,4,8,16,32,64,128,256,514,1050,2240,5158
Number of permutations of 0..(n-1) representable as consecutive sums of 8 
adjacent elements of a sequence of n+7 non-negative integers

1,2,4,8,16,32,64,128,256,512,1026
Number of permutations of 0..(n-1) representable as consecutive sums of 9 
adjacent elements of a sequence of n+8 non-negative integers

more terms to be forthcoming on the final ones.


 rhhardin at mindspring.com
rhhardin at att.net (either)