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).

5, 10, 14, 49, 80, 355, 599, 2764, 4685, 21730, 36854, 171049, 290120, 1346635, 2284079, 10602004, 17982485, 83469370, 141575774, 657152929, 1114623680, 5173754035, 8775413639, 40732879324, 69088685405, 320689280530, 543934069574, 2524781364889

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Index entries for linear recurrences with constant coefficients, signature (1,8,-8,-1,1).

Formula

a(n+4) = 8*a(n+2)-a(n)-27; r15=sqrt(15).

a(n) = ((1+r15)*(4+r15)^((n-1)/2)+(1-r15*(4-r15)^((n-1)/2)+18)/4 for n odd;

a(n) = ((11+3*r15)*(4+r15)^((n-2)/2)+(11-3*r15)*(4-r15)^((n-2)/2)+18)/4 for n even.

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]

Example

for n=4 a(4)=49; b(4)=12; binomial(49,6)=1383816;
binomial(49,4)*binomial(12,2)= 211876*66=1383816;

Maple

n:=1: for m from 1 to 2000 do w:=sqrt(1+60*m*(m-1)):
if (w=floor(w)) then a(n)=(9+w)/2: b(n):=m: inc(n): end if: end do:

Crossrefs

Cf. A105045 (sequence b(n)).

Sequence in context: A258151 A280320 A213365 * A004470 A205688 A080949

Adjacent sequences: A179120 A179121 A179122 * A179124 A179125 A179126

Keyword

nonn,uned,easy

Author

Paul Weisenhorn, Jun 30 2010

Extensions

More terms from Colin Barker, Jan 01 2013

Status

approved