login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
16

%I #17 Nov 04 2016 21:53:26

%S 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,

%T 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,

%U 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

%N 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

%C Table starts

%C .1.1.1..1...1....1.....1.....1.....1......1......1......1.......1.......1

%C .1.1.1..1...1....1.....1.....1.....1......1......1......1.......1.......1

%C .1.1.1..1...2....2.....2.....2.....2......3......3......3.......3.......3

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

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

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

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

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

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

%C .1.2.2.45.860.4751.14387.34449.81289.193997.434662.897102.1742199.3234015

%H R. H. Hardin, <a href="/A184348/b184348.txt">Table of n, a(n) for n = 1..268</a>

%F 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

%e All solutions for n=6 k=5

%e ..0....0

%e ..0....1

%e ..0....0

%e ..0....5

%e ..0....0

%e ..5....4

%p T:= (n,k) -> coeff(mul(add(x^(i^4*j),j=0..k),i=1..n),x,n^4*k):

%p seq(seq(f(n,s-n),n=1..s-1),s=2..15); # _Robert Israel_, Nov 03 2016

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

%K nonn,tabl

%O 1,20

%A _R. H. Hardin_, Jan 11 2011