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).

%I A216635 #8 Jun 02 2025 08:07:46
%S A216635 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,
%T A216635 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,
%U A216635 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
%N 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).
%C A216635 Table starts
%C A216635 .......1......1.....1....1...1..1.1.1.1
%C A216635 .......1......1.....1....1...1..1.1.1.1
%C A216635 .......2......1.....1....1...1..1.1.1.1
%C A216635 .......5......1.....1....1...1..1.1.1.1
%C A216635 ......12......2.....1....1...1..1.1.1.1
%C A216635 ......32......4.....1....1...1..1.1.1.1
%C A216635 ......94.....14.....3....2...1..1.1.1.1
%C A216635 .....289.....37.....8....3...1..1.1.1.1
%C A216635 .....910....105....18....6...1..1.1.1.1
%C A216635 ....2934....309....42...12...1..1.1.1.1
%C A216635 ....9686....939...100...24...1..2.1.1.1
%C A216635 ...32540...2903...265...63...2..2.1.1.1
%C A216635 ..110780...8865...775..164...7..2.1.1.1
%C A216635 ..381676..28163..2241..424..15..5.1.1.1
%C A216635 .1328980..90648..6709.1163..33.11.1.1.1
%C A216635 .4669367.297615.20661.2919.100.18.1.1.1
%H A216635 R. H. Hardin, <a href="/A216635/b216635.txt">Table of n, a(n) for n = 1..325</a>
%e A216635 All solutions for n=8 k=4
%e A216635 ..1....0....0
%e A216635 ..4....1....1
%e A216635 ..4....2....3
%e A216635 ..4....3....3
%e A216635 ..4....4....5
%e A216635 ..5....5....6
%e A216635 ..5....6....6
%e A216635 ..7....7....6
%Y A216635 Column 1 is A002838(n-1)
%Y A216635 sum 1..n instead of 0..n-1: A216645
%K A216635 nonn,tabl
%O A216635 1,6
%A A216635 _R. H. Hardin_ Sep 11 2012