cp's OEIS Frontend

A179123 Place a(n) red and b(n) blue balls in an urn; draw 6 balls without replacement; Probability(6 red balls)=Probability(4 red and 2 blue balls); binomial(a(n),6)=binomial(a(n),4)*binomial(b(n),2).

%I A179123 #26 Feb 09 2025 09:44:19
%S A179123 5,10,14,49,80,355,599,2764,4685,21730,36854,171049,290120,1346635,
%T A179123 2284079,10602004,17982485,83469370,141575774,657152929,1114623680,
%U A179123 5173754035,8775413639,40732879324,69088685405,320689280530,543934069574,2524781364889
%N A179123 Place a(n) red and b(n) blue balls in an urn; draw 6 balls without replacement; Probability(6 red balls)=Probability(4 red and 2 blue balls); binomial(a(n),6)=binomial(a(n),4)*binomial(b(n),2).
%H A179123 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,8,-8,-1,1).
%F A179123 a(n+4) = 8*a(n+2)-a(n)-27; r15=sqrt(15).
%F A179123 a(n) = ((1+r15)*(4+r15)^((n-1)/2)+(1-r15)*(4-r15)^((n-1)/2)+18)/4 for n odd;
%F A179123 a(n) = ((11+3*r15)*(4+r15)^((n-2)/2)+(11-3*r15)*(4-r15)^((n-2)/2)+18)/4 for n even.
%F A179123 a(n) = a(n-1)+8*a(n-2)-8*a(n-3)-a(n-4)+a(n-5). G.f.: -x*(4*x^4-5*x^3-36*x^2+5*x+5) / ((x-1)*(x^4-8*x^2+1)). - _Colin Barker_, Jan 01 2013
%e A179123 for n=4 a(4)=49; b(4)=12; binomial(49,6)=1383816;
%e A179123 binomial(49,4)*binomial(12,2)= 211876*66=1383816;
%p A179123 n:=1: for m from 1 to 2000 do w:=sqrt(1+60*m*(m-1)):
%p A179123 if (w=floor(w)) then a(n)=(9+w)/2: b(n):=m: inc(n): end if: end do:
%Y A179123 Cf. A105045 (sequence b(n)).
%K A179123 nonn,uned,easy
%O A179123 1,1
%A A179123 _Paul Weisenhorn_, Jun 30 2010
%E A179123 More terms from _Colin Barker_, Jan 01 2013