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Number of strings of numbers x(i=1..10) in 0..n with Sum_{i=1..10} i*x(i) = n*10.
1

%I #8 Feb 05 2025 22:03:23

%S 10,142,1066,5439,21310,69331,195760,495251,1146377,2467215,4994696,

%T 9599863,17642702,31185762,53268735,88272866,142374254,224127675,

%U 345174032,521130514,772646635,1126707621,1618154572,2291530676

%N Number of strings of numbers x(i=1..10) in 0..n with Sum_{i=1..10} i*x(i) = n*10.

%H R. H. Hardin, <a href="/A184710/b184710.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n)=2*a(n-2)+a(n-3)-a(n-6)-3*a(n-7)-2*a(n-8)+3*a(n-12)+4*a(n-13)+2*a(n-14)+3*a(n-15)+2*a(n-16)-3*a(n-17)-5*a(n-18)-4*a(n-19)-5*a(n-20)-4*a(n-21)-a(n-22)+2*a(n-23)+4*a(n-24)+6*a(n-25)+6*a(n-26)+4*a(n-27)+2*a(n-28)-a(n-29)-4*a(n-30)-5*a(n-31)-4*a(n-32)-5*a(n-33)-3*a(n-34)+2*a(n-35)+3*a(n-36)+2*a(n-37)+4*a(n-38)+3*a(n-39)-2*a(n-43)-3*a(n-44)-a(n-45)+a(n-48)+2*a(n-49)-a(n-51).

%e Some solutions for n=3:

%e ..0....1....0....0....2....1....0....3....0....0....0....0....3....3....0....1

%e ..1....2....1....3....0....0....1....3....3....2....2....1....0....0....1....3

%e ..0....0....1....1....0....1....0....1....0....0....1....0....3....0....0....2

%e ..1....2....1....0....3....0....1....1....2....3....0....3....2....1....0....0

%e ..0....1....1....1....0....2....2....0....0....0....0....0....0....0....1....0

%e ..0....2....0....0....0....0....0....1....0....1....0....1....0....0....1....0

%e ..1....0....0....1....1....1....2....0....1....0....2....0....0....2....0....1

%e ..1....0....2....0....0....0....0....1....0....1....0....0....0....0....1....0

%e ..1....0....0....1....1....1....0....0....1....0....1....0....0....1....1....0

%e ..0....0....0....0....0....0....0....0....0....0....0....1....1....0....0....1

%Y Row 10 of A184703.

%K nonn,changed

%O 1,1

%A _R. H. Hardin_, Jan 20 2011