cp's OEIS Frontend

A179167 Place a(n) red and b(n) blue balls in an urn; draw 3 balls without replacement; Probability(3 red balls) = Probability(1 red and 2 blue balls); binomial(a(n),3) = binomial(a(n),1)*binomial(b(n),2).

%I A179167 #28 Oct 14 2024 02:59:41
%S A179167 3,4,11,37,134,496,1847,6889,25706,95932,358019,1336141,4986542,
%T A179167 18610024,69453551,259204177,967363154,3610248436,13473630587,
%U A179167 50284273909,187663465046,700369586272,2613814880039,9754889933881
%N A179167 Place a(n) red and b(n) blue balls in an urn; draw 3 balls without replacement; Probability(3 red balls) = Probability(1 red and 2 blue balls); binomial(a(n),3) = binomial(a(n),1)*binomial(b(n),2).
%H A179167 J. Gebel, <a href="/A001014/a001014.txt">Integer points on Mordell curves</a> [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
%H A179167 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,1).
%F A179167 a(n+2) = 4*a(n+1) - a(n) - 3;
%F A179167 a(n+3) = 5*(a(n+2) - a(n+1)) + a(n); r=sqrt(3);
%F A179167 a(n) = (6 + (1+r)*(2+r)^(n-1) + (1-r)*(2-r)^(n-1))/4;
%F A179167 a(n) = ceiling((6 + (1+r)*(2+r)^(n-1))/4).
%F A179167 From _Colin Barker_, Dec 11 2012: (Start)
%F A179167 a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3) for n > 4.
%F A179167 G.f.: x*(x^3-6*x^2+11*x-3) / ((x-1)*(x^2-4*x+1)). (End)
%e A179167 For n=4, a(4)=37; b(4)=21; binomial(37,3) = 7770;
%e A179167 binomial(37,1)*binomial(21,2) = 37*210 = 7770.
%p A179167 r:=sqrt(3): for n from 1 to 40 do
%p A179167 a(n):=(6+(1+r)*(2+r)^(n-1)+(1-r)*(2-r)^(n-1))/4: end do:
%Y A179167 b(n)=A101265(n).
%K A179167 nonn,uned,easy
%O A179167 1,1
%A A179167 _Paul Weisenhorn_, Jun 30 2010