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 A034703 Numbers of the form ((a+b+c) choose a)+((a+b+c) choose b)+((a+b+c) choose c), a,b,c>=1. 1
 9, 14, 20, 25, 27, 35, 41, 44, 45, 54, 63, 65, 77, 90, 92, 104, 119, 126, 129, 134, 135, 140, 152, 170, 175, 189, 198, 209, 219, 230, 231, 246, 252, 261, 275, 298, 299, 300, 324, 340, 350, 377, 405, 417, 434, 440, 450, 464, 465, 469, 472, 495, 506, 527, 560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS MATHEMATICA 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 *) PROG (PARI) tsum(a, b, c)=binomial(a+b+c, a)+binomial(a+b+c, b)+binomial(a+b+c, c) 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} CROSSREFS Sequence in context: A244466 A171123 A173792 * A006624 A184218 A272527 Adjacent sequences:  A034700 A034701 A034702 * A034704 A034705 A034706 KEYWORD nonn AUTHOR EXTENSIONS Definition clarified and PARI program added by Michael B. Porter, Mar 03 2010 STATUS approved

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