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A221235 Number of nonnegative integer arrays of length n summing to n without adjacent equal values.

%I A221235 #15 Apr 28 2022 07:53:51
%S A221235 1,1,2,7,14,30,76,188,444,1075,2656,6504,15926,39316,97252,240597,
%T A221235 596686,1482971,3689768,9191590,22927718,57253334,143101896,358003469,
%U A221235 896391914,2246149936,5632310800,14132640565,35483595966,89141668532,224061612932,563473301874
%N A221235 Number of nonnegative integer arrays of length n summing to n without adjacent equal values.
%H A221235 Alois P. Heinz, <a href="/A221235/b221235.txt">Table of n, a(n) for n = 0..500</a> (first 210 terms from R. H. Hardin)
%F A221235 a(n) = A106351(2n,n). - _Alois P. Heinz_, Oct 12 2017
%e A221235 All solutions for n=3
%e A221235 ..1....2....0....2....0....0....1
%e A221235 ..2....1....3....0....2....1....0
%e A221235 ..0....0....0....1....1....2....2
%p A221235 b:= proc(n, h, t) option remember; `if`(t<2, `if`(n<>h, 1, 0),
%p A221235       add(`if`(h=j, 0, b(n-j, `if`(j>n-j, -1, j), t-1)), j=0..n))
%p A221235     end:
%p A221235 a:= n-> b(n, -1, n):
%p A221235 seq(a(n), n=0..35);  # _Alois P. Heinz_, Oct 15 2017
%t A221235 b[n_, h_, t_] := b[n, h, t] = If[t < 2, If[n != h, 1, 0],
%t A221235      Sum[If[h == j, 0, b[n-j, If[j > n-j, -1, j], t-1]], {j, 0, n}]];
%t A221235 a[n_] := b[n, -1, n];
%t A221235 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Apr 28 2022, after _Alois P. Heinz_ *)
%Y A221235 Cf. A106351.
%K A221235 nonn
%O A221235 0,3
%A A221235 _R. H. Hardin_, Jan 10 2013
%E A221235 a(0)=1 prepended by _Alois P. Heinz_, Oct 15 2017