A184348 Table read by antidiagonals: T(n,k) is the number of strings of numbers x(i=1..n) in 0..k with sum i^4*x(i) equal to n^4*k

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 1, 2, 1, 4, 2, 5, 1, 2, 1, 1, 1, 2, 2, 7, 7, 9, 2, 4, 2, 1, 1, 1, 3, 3, 8, 16, 17, 26, 20, 2, 2, 1, 1, 1, 3, 4, 12, 47, 45, 200, 79, 45, 25, 1, 1, 1, 1, 3, 6, 18, 90, 124

Offset

1,20

Comments

Table starts

.1.1.1..1...1....1.....1.....1.....1......1......1......1.......1.......1

.1.1.1..1...1....1.....1.....1.....1......1......1......1.......1.......1

.1.1.1..1...2....2.....2.....2.....2......3......3......3.......3.......3

.1.1.1..1...1....1.....1.....2.....3......4......6......9......11......14

.1.2.2..3...3....4.....7.....8....12.....18.....29.....40......60......80

.1.1.1..1...2....7....16....47....90....137....203....295.....412.....584

.1.1.2..5...9...17....45...124...307....654...1211...2023....3151....4750

.1.1.1..2..26..200...628..1371..2578...4737...8602..15219...25591...41530

.1.2.4.20..79..353..1612..5439.14366..31892..63524.118564..212692..367954

.1.2.2.45.860.4751.14387.34449.81289.193997.434662.897102.1742199.3234015

Links

R. H. Hardin, Table of n, a(n) for n = 1..268

Formula

T(n,k) is the coefficient of x^(k*n^4) in Product_{i=1..n} Sum_{j=0..k} x^(j*i^4). - Robert Israel, Nov 03 2016

Example

All solutions for n=6 k=5
..0....0
..0....1
..0....0
..0....5
..0....0
..5....4

Maple

T:= (n, k) -> coeff(mul(add(x^(i^4*j), j=0..k), i=1..n), x, n^4*k):
seq(seq(f(n, s-n), n=1..s-1), s=2..15); # Robert Israel, Nov 03 2016

Crossrefs

Cf. A184339 (diagonal), A184340 - A184347 (columns 1 to 8), A184349 - A184354 (rows 3 to 8).

Sequence in context: A329443 A348416 A263025 * A307614 A363057 A242481

Adjacent sequences: A184345 A184346 A184347 * A184349 A184350 A184351

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 11 2011

Status

approved