Search: id:A089508
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%I A089508
%S A089508 1,14,103,713,4894,33551,229969,1576238,10803703,74049689,507544126,
%T A089508 3478759199,23843770273,163427632718,1120149658759,7677619978601,
%U A089508 52623190191454,360684711361583,2472169789339633,16944503814015854
%N A089508 Solution to a binomial problem together with companion sequence A081016(n-1).
%C A089508 a(n) and b(n) := A081016(n-1) are the solutions to the Diophantine equation 
               binomial(a,b)=binomial(a+1,b-1). The first few binomials are given 
               by A090162(n).
%D A089508 A. I. Shirshov: On the equation binomial(n,m)=binomial(n+1,m-1), pp. 
               83-86, in: Kvant Selecta: Algebra and Analysis, I, ed. S. Tabachnikov, 
               Am.Math.Soc., 1999
%F A089508 G.f.: x*(1+6*x-x^2)/((1-x)*(1-7*x+x^2)).
%F A089508 a(n)=A081018(n)-1 = F(2*n)*F(2*n+1)-1, n>=1; with F(n) := A000045(n) 
               (Fibonacci).
%e A089508 n = 2: a(2) = 14, b(2) = A081016(1) = 6 satisfy binomial(14,6) = 3003 
               = binomial(15,5). 3003 = A090162(2).
%Y A089508 Equals A081018 - 1.
%Y A089508 Sequence in context: A041370 A055913 A005757 this_sequence A131709 A139614 
               A068390
%Y A089508 Adjacent sequences: A089505 A089506 A089507 this_sequence A089509 A089510 
               A089511
%K A089508 nonn,easy
%O A089508 1,2
%A A089508 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Dec 01 2003

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