A230196 - OEIS

%I #31 Sep 08 2022 08:46:06

%S 0,0,0,0,0,0,1,1,1,0,2,1,2,2,1,2,3,2,3,2,3,3,4,3,3,4,4,4,5,3,5,5,5,5,

%T 5,5,6,6,6,5,7,6,7,7,6,7,8,7,8,7,8,8,9,8,8,9,9,9,10,8,10,10,10,10,10,

%U 10,11,11,11,10,12,11,12,12,11,12,13,12,13,12,13,13,14,13,13,14,14,14,15,13,15,15,15,15,15,15,16,16,16

%N Number of pairs (p,q) such that 2*p + 3*q = n and p != q.

%H Vincenzo Librandi, <a href="/A230196/b230196.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1,1,1,1,0,-1,-1).

%F a(n) = floor((n+1)/6)+floor((n-1)/6)-floor(n/6)+floor((n-1)/5)-floor(n/5).

%F G.f.: x*(2*x^8 + 2*x^7 + x^6)/((1+x)*(1-x^3)*(1-x^5)). - _Ralf Stephan_, Oct 12 2013

%F a(n) = floor((n-3)/2)-floor((n-3)/3)+floor((n-1)/5)-floor(n/5). - _Mircea Merca_, Nov 27 2013

%p seq(floor((n+1)*(1/6))+floor((n-1)*(1/6))-floor((1/6)*n)+floor((n-1)*(1/5))-floor((1/5)*n),n=1..99)

%t CoefficientList[Series[(2 x^8 + 2 x^7 + x^6)/((1 + x) (1 - x^3) (1 - x^5)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Oct 13 2013 *)

%o (Magma) [Floor((n+1)*(1/6))+Floor((n-1)*(1/6))-Floor((1/6)*n)+Floor((n-1)*(1/5))-Floor((1/5)*n): n in [1..80]]; // _Vincenzo Librandi_, Oct 13 2013

%K nonn,easy

%O 1,11

%A _Mircea Merca_, Oct 11 2013