|
%I #18 Aug 03 2014 14:01:40
%S 12,16,20,21,25,26,27,30,31,34,35,36,38,40,41,42,43,45,46,48,49,50,51,
%T 55,56,57,60,61,62,63,64,65,66,70,71,72,73,75,76,77,80,81,83,84,85,86,
%U 87,88,90,91,92,93,94,97,98,99,100,101,102,104,105,106,110
%N Natural numbers equal to the sum of two nontrivial binomial coefficients, sorted, duplicates removed.
%C Nontrivial binomial coefficients are C(n,k) with 2 <= k <= n-2.
%H Charles R Greathouse IV, <a href="/A210577/b210577.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 12 since 6 is the lowest nontrivial binomial coefficient and 6+6 = 12.
%t lim = 110; bc = {}; n = 4; While[c = Select[Binomial[n, Range[2, Floor[n/2]]], # <= lim &]; Length[c] > 0, bc = Join[bc, c]; n++]; bc = Sort[bc]; Select[Union[Flatten[Outer[Plus, bc, bc]]], # <= lim &] (* _T. D. Noe_, Mar 22 2012 *)
%o (PARI) list(lim)=my(v=List(), t, u=v); for(n=4, sqrtint(2*lim)+1, for(k=2, n\2, t=binomial(n, k); if(t>lim, break, listput(v, t)))); v=vecsort(Vec(v), , 8); for(i=1,#v,for(j=1,i,if(v[i]+v[j]>lim,break,listput(u,v[i]+v[j]))));vecsort(Vec(u),,8) \\ _Charles R Greathouse IV_, Apr 03 2012
%Y Two-term sums of members of A006987.
%Y Cf. A007318.
%K easy,nonn
%O 1,1
%A _Douglas Latimer_, Mar 22 2012
|
