cp's OEIS Frontend

A221321 T(n,k)=Number of nonnegative integer arrays of length n summing to n without equal adjacent values modulo k.

%I A221321 #6 Jul 23 2025 01:50:41
%S A221321 1,1,0,1,0,0,1,2,3,0,1,2,6,8,0,1,2,7,8,5,0,1,2,7,14,19,0,0,1,2,7,14,
%T A221321 28,44,28,0,1,2,7,14,30,66,84,72,0,1,2,7,14,30,76,168,212,45,0,1,2,7,
%U A221321 14,30,76,185,378,474,0,0,1,2,7,14,30,76,188,430,866,1008,286,0,1,2,7,14,30,76
%N A221321 T(n,k)=Number of nonnegative integer arrays of length n summing to n without equal adjacent values modulo k.
%C A221321 Table starts
%C A221321 .1...1....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1
%C A221321 .0...0....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
%C A221321 .0...3....6.....7.....7.....7.....7.....7.....7.....7.....7.....7.....7.....7
%C A221321 .0...8....8....14....14....14....14....14....14....14....14....14....14....14
%C A221321 .0...5...19....28....30....30....30....30....30....30....30....30....30....30
%C A221321 .0...0...44....66....76....76....76....76....76....76....76....76....76....76
%C A221321 .0..28...84...168...185...188...188...188...188...188...188...188...188...188
%C A221321 .0..72..212...378...430...444...444...444...444...444...444...444...444...444
%C A221321 .0..45..474...866..1044..1071..1075..1075..1075..1075..1075..1075..1075..1075
%C A221321 .0...0.1008..2128..2544..2638..2656..2656..2656..2656..2656..2656..2656..2656
%C A221321 .0.286.2438..5065..6154..6460..6499..6504..6504..6504..6504..6504..6504..6504
%C A221321 .0.728.5436.12000.15002.15756.15904.15926.15926.15926.15926.15926.15926.15926
%H A221321 R. H. Hardin, <a href="/A221321/b221321.txt">Table of n, a(n) for n = 1..2347</a>
%e A221321 Some solutions for n=7 k=4
%e A221321 ..1....0....0....0....0....3....1....0....2....0....0....0....1....3....0....2
%e A221321 ..2....1....1....3....1....0....2....3....0....3....1....1....0....1....1....1
%e A221321 ..0....0....0....0....0....1....1....0....1....1....0....0....3....0....0....0
%e A221321 ..1....2....3....1....1....0....0....2....0....0....1....1....1....2....1....3
%e A221321 ..2....3....0....2....2....1....1....1....3....1....4....0....0....0....0....0
%e A221321 ..1....1....2....1....0....0....2....0....0....2....1....5....2....1....1....1
%e A221321 ..0....0....1....0....3....2....0....1....1....0....0....0....0....0....4....0
%Y A221321 Diagonal is A221235 for n>3
%K A221321 nonn,tabl
%O A221321 1,8
%A A221321 _R. H. Hardin_ Jan 10 2013