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%I #12 Nov 05 2016 08:15:58
%S 1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,5,6,7,9,9,9,9,10,11,11,11,11,12,13,
%T 13,13,14,16,18,19,20,21,23,25,25,25,26,27,28,28,28,29,31,33,34,35,37,
%U 39,41,42,43,45,47,49,49,50,51,52,54,55,57,59,61,63,64,66,68,70,72,73,75,77,79
%N Number of strings of numbers x(i=1..3) in 0..n with sum i^4*x(i) equal to 81*n.
%C Row 3 of A184348
%H R. H. Hardin, <a href="/A184349/b184349.txt">Table of n, a(n) for n = 1..998</a>
%H Robert Israel, <a href="/A184349/a184349.pdf">Proof of formula</a>
%F Empirical: a(n) = 2*a(n-1)-a(n-2)+a(n-81)-2*a(n-82)+a(n-83).
%F Coefficient of x^(81n) in h(x^(n+1))/h(x), where h(x) = (x-1)(x^16-1)(x^81-1). - _Robert Israel_, Nov 03 2016
%e All solutions for n=5
%e ..0....1
%e ..0....5
%e ..5....4
%p h:= unapply((x-1)*(x^16-1)*(x^81-1),x):
%p f:= n -> coeff(normal(h(x^(n+1))/h(x)), x, 81*n):
%p map(f, [$1..100]); # _Robert Israel_, Nov 03 2016
%K nonn
%O 1,5
%A _R. H. Hardin_, Jan 11 2011
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