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%I #11 Oct 30 2018 03:32:48
%S 9,14,20,25,27,35,41,44,45,54,63,65,77,90,92,104,119,126,129,134,135,
%T 140,152,170,175,189,198,209,219,230,231,246,252,261,275,298,299,300,
%U 324,340,350,377,405,417,434,440,450,464,465,469,472,495,506,527,560
%N Numbers of the form binomial(a+b+c, a) + binomial(a+b+c, b) + binomial(a+b+c, c), with a,b,c >= 1.
%t pr[{a_,b_,c_}]:=Module[{t=a+b+c},Binomial[t,a]+Binomial[t,b]+ Binomial[ t,c]]; With[{nn=60},Take[pr/@Tuples[Range[nn],3]//Union,nn]] (* _Harvey P. Dale_, Oct 13 2016 *)
%o (PARI) tsum(a,b,c)=binomial(a+b+c,a)+binomial(a+b+c,b)+binomial(a+b+c,c)
%o isA034703(n) = {local(r,a,b,c);r=0;a=1;b=1;c=1;while(tsum(a,1,1)<=n,while(tsum(a,b,1)<=n,while(tsum(a,b,c)<=n,if(tsum(a,b,c)==n,r=1);c=c+1);b=b+1;c=1);a=a+1;b=1;c=1);r} // _Michael B. Porter_, Mar 03 2010
%K nonn
%O 1,1
%A _Erich Friedman_
%E Definition clarified by _Michael B. Porter_, Mar 03 2010
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