A216635 -id:A216635 - cp's OEIS frontend

A216645 T(n,k)=Number of nondecreasing arrays of n 1..n integers with the sum of their k powers equal to sum(i^k,i=1..n).

1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 32, 1, 1, 1, 1, 1, 3, 94, 1, 1, 1, 1, 1, 2, 8, 289, 1, 1, 1, 1, 1, 1, 2, 25, 910, 1, 1, 1, 1, 1, 1, 2, 6, 83, 2934, 1, 1, 1, 1, 1, 1, 1, 2, 12, 257, 9686, 1, 1, 1, 1, 1, 1, 1, 1, 5, 30, 788, 32540, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 76, 2491

Offset: 1

R. H. Hardin Sep 11 2012

Table starts
.......1......1.....1....1..1..1.1
.......1......1.....1....1..1..1.1
.......2......1.....1....1..1..1.1
.......5......1.....1....1..1..1.1
......12......1.....1....1..1..1.1
......32......3.....2....1..1..1.1
......94......8.....2....2..1..1.1
.....289.....25.....6....2..1..1.1
.....910.....83....12....5..1..1.1
....2934....257....30...11..1..2.1
....9686....788....76...25..1..2.1
...32540...2491...224...51..2..2.1
..110780...7885...597..136..4..2.1
..381676..25099..1801..367..8..3.1
.1328980..80481..5469..886.21..3.1
.4669367.264505.16958.2507.45.14.1

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

R. H. Hardin, Table of n, a(n) for n = 1..291

Column 1 is A002838(n-1)

sum 0..n-1 instead of 1..n: A216635

A216630 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 2nd powers equal to sum(i^2,i=0..n-1).

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 14, 37, 105, 309, 939, 2903, 8865, 28163, 90648, 297615, 989077, 3320885, 11280835, 38583017, 133018026, 461630411, 1612842357, 5667628973, 20019876401, 71078302590, 253504107762, 908014000543, 3265037780657

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 2 of A216635

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

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

A216631 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 3rd powers equal to sum(i^3,i=0..n-1).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 3, 8, 18, 42, 100, 265, 775, 2241, 6709, 20661, 64264, 202154, 647838, 2095932, 6861091, 22703554, 75731878, 254656486, 862839461, 2942117884, 10094669306, 34837009237, 120849420979, 421291017964, 1475463672293

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 3 of A216635

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

A216632 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 4th powers equal to sum(i^4,i=0..n-1).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 3, 6, 12, 24, 63, 164, 424, 1163, 2919, 8289, 24060, 70704, 212130, 672520, 2080293, 6485878, 20449084

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 4 of A216635

			All solutions for n=9
..1....0....0....0....0....0
..4....0....1....1....0....0
..4....1....2....3....1....3
..4....3....3....3....2....3
..4....6....4....5....4....3
..5....6....5....6....6....3
..5....6....6....6....7....4
..7....7....7....6....7....8
..8....7....8....8....7....8

A216633 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 5th powers equal to sum(i^5,i=0..n-1).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7, 15, 33, 100, 265, 744, 2174, 6293, 18854

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 5 of A216635

			All solutions for n=12
..0....0
..0....1
..1....2
..4....3
..5....4
..5....5
..6....6
..6....7
..9....8
.10....9
.10...10
.10...11

A216634 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 6th powers equal to sum(i^6,i=0..n-1).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5, 11, 18, 50, 113, 257, 678, 1814

Offset: 1

R. H. Hardin Sep 11 2012

nonn

Column 6 of A216635

			All solutions for n=11
..0....0
..1....1
..2....2
..2....3
..2....4
..4....5
..7....6
..8....7
..9....8
..9....9
..9...10

cp's OEIS Frontend

A216645 T(n,k)=Number of nondecreasing arrays of n 1..n integers with the sum of their k powers equal to sum(i^k,i=1..n).

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A216630 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 2nd powers equal to sum(i^2,i=0..n-1).

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A216631 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 3rd powers equal to sum(i^3,i=0..n-1).

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A216632 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 4th powers equal to sum(i^4,i=0..n-1).

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A216633 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 5th powers equal to sum(i^5,i=0..n-1).

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A216634 Number of nondecreasing arrays of n 0..n-1 integers with the sum of their 6th powers equal to sum(i^6,i=0..n-1).

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