A216645 -id:A216645 - cp's OEIS frontend

A216635 T(n,k)=Number of nondecreasing arrays of n 0..n-1 integers with the sum of their k'th powers equal to sum(i^k,i=0..n-1).

1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 1, 12, 1, 1, 1, 1, 2, 32, 1, 1, 1, 1, 1, 4, 94, 1, 1, 1, 1, 1, 1, 14, 289, 1, 1, 1, 1, 1, 1, 3, 37, 910, 1, 1, 1, 1, 1, 1, 2, 8, 105, 2934, 1, 1, 1, 1, 1, 1, 1, 3, 18, 309, 9686, 1, 1, 1, 1, 1, 1, 1, 1, 6, 42, 939, 32540, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 100, 2903

Offset: 1

R. H. Hardin Sep 11 2012

Table starts
.......1......1.....1....1...1..1.1.1.1
.......1......1.....1....1...1..1.1.1.1
.......2......1.....1....1...1..1.1.1.1
.......5......1.....1....1...1..1.1.1.1
......12......2.....1....1...1..1.1.1.1
......32......4.....1....1...1..1.1.1.1
......94.....14.....3....2...1..1.1.1.1
.....289.....37.....8....3...1..1.1.1.1
.....910....105....18....6...1..1.1.1.1
....2934....309....42...12...1..1.1.1.1
....9686....939...100...24...1..2.1.1.1
...32540...2903...265...63...2..2.1.1.1
..110780...8865...775..164...7..2.1.1.1
..381676..28163..2241..424..15..5.1.1.1
.1328980..90648..6709.1163..33.11.1.1.1
.4669367.297615.20661.2919.100.18.1.1.1

			All solutions for n=8 k=4
..1....0....0
..4....1....1
..4....2....3
..4....3....3
..4....4....5
..5....5....6
..5....6....6
..7....7....6

R. H. Hardin, Table of n, a(n) for n = 1..325

Column 1 is A002838(n-1)

sum 1..n instead of 0..n-1: A216645

A216640 Number of nondecreasing arrays of n 1..n integers with the sum of their 2nd powers equal to sum(i^2,i=1..n).

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 8, 25, 83, 257, 788, 2491, 7885, 25099, 80481, 264505, 884517, 2994535, 10208806, 35095825, 121699761, 424273761, 1487693075, 5244197347, 18584820912, 66169376686, 236592018517, 849466213882, 3061492852986, 11072927827447

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 2 of A216645

			All solutions for n=6
..1....3....1
..2....3....1
..3....4....1
..4....4....4
..5....4....6
..6....5....6

R. H. Hardin, Table of n, a(n) for n = 1..49

A216641 Number of nondecreasing arrays of n 1..n integers with the sum of their 3rd powers equal to sum(i^3,i=1..n).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 6, 12, 30, 76, 224, 597, 1801, 5469, 16958, 53308, 169872, 548344, 1791949, 5915441, 19700851, 66148464, 223751776, 761919971, 2610778118, 8998428171, 31179152130, 108577507149, 379879051198

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 3 of A216645

			All solutions for n=8
..1....3....1....2....2....1
..1....4....2....2....2....2
..4....5....2....2....4....3
..5....6....5....3....4....4
..5....6....5....6....4....5
..5....6....7....7....4....6
..7....6....7....7....8....7
..8....6....7....7....8....8

A216642 Number of nondecreasing arrays of n 1..n integers with the sum of their 4th powers equal to sum(i^4,i=1..n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 2, 5, 11, 25, 51, 136, 367, 886, 2507, 6986, 20453, 60708, 172073, 524771, 1628140, 5085497

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 4 of A216645

			All solutions for n=9
..3....1....1....1....1
..3....3....2....1....1
..4....3....3....2....1
..5....5....4....2....2
..6....6....5....4....5
..7....6....6....5....7
..7....6....7....6....8
..8....8....8....9....8
..8....9....9....9....8

A216643 Number of nondecreasing arrays of n 1..n integers with the sum of their 5th powers equal to sum(i^5,i=1..n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 21, 45, 159, 483, 1397, 4252, 12860

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 5 of A216645

			All solutions for n=12
..1....2
..2....3
..3....3
..4....3
..5....5
..6....5
..7....6
..8....8
..9...10
.10...11
.11...11
.12...11

A216644 Number of nondecreasing arrays of n 1..n integers with the sum of their 6th powers equal to sum(i^6,i=1..n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 14, 32, 61, 166, 426, 1009

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 6 of A216645

			All solutions for n=11
..1....1
..2....2
..3....2
..4....2
..5....4
..6....7
..7....8
..8....9
..9....9
.10....9
.11...11

cp's OEIS Frontend

A216635 T(n,k)=Number of nondecreasing arrays of n 0..n-1 integers with the sum of their k'th powers equal to sum(i^k,i=0..n-1).

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A216640 Number of nondecreasing arrays of n 1..n integers with the sum of their 2nd powers equal to sum(i^2,i=1..n).

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A216641 Number of nondecreasing arrays of n 1..n integers with the sum of their 3rd powers equal to sum(i^3,i=1..n).

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A216642 Number of nondecreasing arrays of n 1..n integers with the sum of their 4th powers equal to sum(i^4,i=1..n).

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Examples

A216643 Number of nondecreasing arrays of n 1..n integers with the sum of their 5th powers equal to sum(i^5,i=1..n).

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Comments

Examples

A216644 Number of nondecreasing arrays of n 1..n integers with the sum of their 6th powers equal to sum(i^6,i=1..n).

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Examples