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A034703
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Numbers of the form binomial(a+b+c, a) + binomial(a+b+c, b) + binomial(a+b+c, c), with a,b,c >= 1.
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1
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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
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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} // Michael B. Porter, Mar 03 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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