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%I #13 Nov 18 2020 06:51:17
%S 1,0,2,8,10,22,58,112,219,466,920,1787,3600,7025,13532,26315,50625,
%T 96775,185000,351714,665942,1258649,2371219,4454004,8348735,15612146,
%U 29128863,54245790,100828939,187074952,346527510,640878692,1183480187
%N Number of compositions of n with exactly 2 adjacent equal parts (2 pairs or 1 triple.).
%H Alois P. Heinz, <a href="/A106358/b106358.txt">Table of n, a(n) for n = 3..1000</a>
%H A. Knopfmacher and H. Prodinger, <a href="https://doi.org/10.1006/eujc.1998.0216">On Carlitz compositions</a>, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.
%F a(n) ~ c * d^n * n^2, where d = 1.7502412917183090312497386246... (see A241902), c = 0.0025523594118210599072896951... . - _Vaclav Kotesovec_, Aug 25 2014
%p b:= proc(n, v) option remember; `if`(n=0, [1, 0$2], add((
%p p->`if`(i=v, [0, p[1..2][]], p))(b(n-i, i)), i=1..n))
%p end:
%p a:= n-> b(n, 0)[3]:
%p seq(a(n), n=3..45); # _Alois P. Heinz_, Jun 24 2014
%t b[n_, v_] := b[n, v] = If[n==0, {1, 0, 0}, Sum[If[i==v, Prepend[#[[1;;2]], 0], #]&[b[n-i, i]], {i, 1, n}]];
%t a[n_] := b[n, 0][[3]];
%t a /@ Range[3, 45] (* _Jean-François Alcover_, Nov 18 2020, after _Alois P. Heinz_ *)
%Y Column 2 of A106356. Cf. A003242.
%Y Cf. A241902.
%K nonn
%O 3,3
%A _Christian G. Bower_, Apr 29 2005
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