cp's OEIS Frontend

A131661 Number of compositions of n such that the cardinality of the set of parts is 2.

%I A131661 #18 May 26 2014 04:27:39
%S A131661 0,0,2,5,14,22,44,68,107,172,261,396,606,950,1414,2238,3418,5411,8368,
%T A131661 13297,20840,33268,52549,84120,133775,214611,343025,551064,883600,
%U A131661 1421767,2284870,3680296,5924725,9551161,15393855,24834827,40061700
%N A131661 Number of compositions of n such that the cardinality of the set of parts is 2.
%H A131661 Alois P. Heinz, <a href="/A131661/b131661.txt">Table of n, a(n) for n = 1..1000</a>
%F A131661 G.f.: Sum(Sum(x^(i+j)*(x^i+x^j-2)/((x^i-1)*(x^j-1)*(x^i+x^j-1)), j=1..i-1), i=2..infinity).
%F A131661 a(n) ~ 1/sqrt(5) * ((1+sqrt(5))/2)^(n+1). - _Vaclav Kotesovec_, May 01 2014
%p A131661 with(numtheory):
%p A131661 a:= n-> add(add(add(binomial(j+(n-i*j)/d, j), d=select(x->x<i,
%p A131661         divisors(n-i*j))), j=1..n/i), i=2..n-1):
%p A131661 seq(a(n), n=0..50);  # _Alois P. Heinz_, Feb 01 2014
%t A131661 Rest@ CoefficientList[ Series[ Sum[ x^(i + j)*(x^i + x^j - 2)/((x^i - 1)*(x^j - 1)*(x^i + x^j - 1)), {i, 2, 37}, {j, i - 1}], {x, 0, 37}], x] (* _Robert G. Wilson v_, Sep 16 2007 *)
%Y A131661 Cf. A000005, A002133, A005772, A088142.
%Y A131661 Column k=2 of A235998.
%Y A131661 Cf. A242900 (with distinct multiplicities).
%K A131661 easy,nonn
%O A131661 1,3
%A A131661 _Vladeta Jovovic_, Sep 13 2007
%E A131661 More terms from _Robert G. Wilson v_, Sep 16 2007