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%I #18 Feb 22 2017 20:40:39
%S 1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,
%T 1,1,2,1,1,1,2,1,1,1,2,2,1,1,2,2,1,1,2,2,2,1,2,2,2,1,2,2,2,2,2,2,2,2,
%U 2,2,2,2,3,2,2,2,3,2,2,2,3,3,2,2,3,3,2
%N a(n) = number of pairs (p,q) such that 4*p + 9*q = n.
%C From _Reinhard Zumkeller_, Nov 07 2009: (Start)
%C In other words: number of partitions into 4 or 9;
%C a(n) <= A078134(n); a(A078135(n)) = 0;
%C a(A167632(n)) = n and a(m) < n for m < A167632(n). (End)
%H Reinhard Zumkeller, <a href="/A033183/b033183.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1).
%F a(n) = [ 7 n/9 ]+1+[ -3 n/4 ].
%F G.f.: 1/((1-x^4)*(1-x^9)). - _Vladeta Jovovic_, Nov 12 2004
%F a(n) = a(n-4) + a(n-9) - a(n-13). - _R. J. Mathar_, Dec 04 2011
%t CoefficientList[Series[1/((1-x^4)(1-x^9)),{x,0,80}],x] (* or *) LinearRecurrence[{0,0,0,1,0,0,0,0,1,0,0,0,-1}, {1,0,0,0,1,0,0,0,1,1,0,0,1}, 80] (* _Harvey P. Dale_, Oct 13 2012 *)
%Y Cf. A033182.
%K nonn
%O 0,37
%A Michel Tixier (tixier(AT)dyadel.net)
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