[seqfan] Re: Permutations constructable from consecutive sums

Ron Hardin rhhardin at att.net
Sun Aug 15 15:14:57 CEST 2010


updated with additions (all offset 1)

1,2,4,12,44,176,768,4000,22896,142336,967040,7258368,57919872,490253312,
4455645952,43468799232,445393216256
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,
4315386
Number of permutations of 0..(n-1) representable as consecutive sums of 6 
adjacent elements of a sequence of n+5 non-negative integers

1,2,4,8,16,32,64,128,258,536,1190,2918,7954,23914,76404
Number of permutations of 0..(n-1) representable as consecutive sums of 7 
adjacent elements of a sequence of n+6 non-negative integers

1,2,4,8,16,32,64,128,256,514,1050,2240,5158,13112
Number of permutations of 0..(n-1) representable as consecutive sums of 8 
adjacent elements of a sequence of n+7 non-negative integers

1,2,4,8,16,32,64,128,256,512,1026,2076
Number of permutations of 0..(n-1) representable as consecutive sums of 9 
adjacent elements of a sequence of n+8 non-negative integers

1,2,4,6,12,36,102,324,972,3190,12610,50254,214510,1000260,4848796,
24798190
Number of permutations of 0..(n-1) representable as 1,2,1-weighted consecutive 
sums of 3 adjacent elements of a sequence of n+2 non-negative integers

1,2,2,2,2,2,4,26,38,92,186,356,938,2682,7032,25282,82022,212058,772436
Number of permutations of 0..(n-1) representable as 1,3,3,1-weighted consecutive 
sums of 4 adjacent elements of a sequence of n+3 non-negative integers

1,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,12,48,176,444,420,2124,8056
Number of permutations of 0..(n-1) representable as 1,4,6,4,1-weighted 
consecutive sums of 5 adjacent elements of a sequence of n+4 non-negative 
integers

the 12 integer sequences for n=17
3 0 0 0 0 0 1 0 1 0 2 0 0 2 1 0 0 0 1 1 5
3 0 0 0 0 0 1 2 0 0 2 0 1 0 1 0 0 0 1 1 5
1 1 0 0 0 1 0 1 0 2 0 0 2 1 0 0 0 0 0 3 3
1 1 0 0 0 1 2 0 0 2 0 1 0 1 0 0 0 0 0 3 3
7 1 0 0 0 0 0 2 1 0 0 1 0 0 0 2 0 1 0 2 3
7 1 0 0 0 2 1 0 0 1 0 0 0 0 0 2 0 1 0 2 3
5 1 1 0 0 0 1 0 1 0 2 0 0 2 1 0 0 0 0 0 3
5 1 1 0 0 0 1 2 0 0 2 0 1 0 1 0 0 0 0 0 3
3 3 0 0 0 0 0 1 0 1 0 2 0 0 2 1 0 0 0 1 1
3 3 0 0 0 0 0 1 2 0 0 2 0 1 0 1 0 0 0 1 1
3 2 0 1 0 2 0 0 0 0 0 1 0 0 1 2 0 0 0 1 7
3 2 0 1 0 2 0 0 0 1 0 0 1 2 0 0 0 0 0 1 7
giving the 12 permutations
3 0 1 4 7 8 9 12 13 10 11 16 14 6 2 5 15
3 0 1 6 14 16 11 10 13 12 9 8 7 4 2 5 15
5 2 4 7 8 9 12 13 10 11 16 14 6 1 0 3 15
5 2 6 14 16 11 10 13 12 9 8 7 4 1 0 3 15
11 1 0 2 9 16 14 7 5 6 4 3 8 13 12 10 15
11 3 9 16 14 7 5 6 4 1 0 2 8 13 12 10 15
15 5 2 4 7 8 9 12 13 10 11 16 14 6 1 0 3
15 5 2 6 14 16 11 10 13 12 9 8 7 4 1 0 3
15 3 0 1 4 7 8 9 12 13 10 11 16 14 6 2 5
15 3 0 1 6 14 16 11 10 13 12 9 8 7 4 2 5
15 10 12 13 8 2 0 1 4 6 5 7 14 16 9 3 11
15 10 12 13 8 3 4 6 5 7 14 16 9 2 0 1 11



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





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