A179167 a(n) is the number of red balls in an urn such that if the urn contains b(n)=A101265(n) blue balls, the probability of drawing 3 red balls without replacement is the same as drawing 1 red and 2 blue balls without replacement; that is, binomial(a(n),3) = binomial(a(n),1) * binomial(b(n),2).

3, 4, 11, 37, 134, 496, 1847, 6889, 25706, 95932, 358019, 1336141, 4986542, 18610024, 69453551, 259204177, 967363154, 3610248436, 13473630587, 50284273909, 187663465046, 700369586272, 2613814880039, 9754889933881, 36405744855482, 135868089488044, 507066613096691

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Index entries for linear recurrences with constant coefficients, signature (5,-5,1).

Formula

From Colin Barker, Dec 11 2012: (Start)

a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3) for n > 4.

G.f.: x*(x^3-6*x^2+11*x-3) / ((x-1)*(x^2-4*x+1)). (End)

Example

For n=4, a(4)=37; b(4)=21; binomial(37,3) = 7770;
binomial(37,1)*binomial(21,2) = 37*210 = 7770.

Maple

r:=sqrt(3): for n from 1 to 40 do
a(n):=(6+(1+r)*(2+r)^(n-1)+(1-r)*(2-r)^(n-1))/4: end do:

Mathematica

LinearRecurrence[{5, -5, 1}, {3, 4, 11, 37}, 30] (* Paolo Xausa, Apr 22 2026 *)

Crossrefs

Cf. A101265 (sequence b(n)).

Sequence in context: A275309 A119042 A042273 * A259845 A037185 A299047

Adjacent sequences: A179164 A179165 A179166 * A179168 A179169 A179170

Keyword

nonn,easy

Author

Paul Weisenhorn, Jun 30 2010

Extensions

Edited by Sean A. Irvine, Apr 22 2026

More terms from Paolo Xausa, Apr 22 2026

Status

approved