A210578 Natural numbers that can be expressed as the sum of one or two nontrivial binomial coefficients, sorted, duplicates removed.

6, 10, 12, 15, 16, 20, 21, 25, 26, 27, 28, 30, 31, 34, 35, 36, 38, 40, 41, 42, 43, 45, 46, 48, 49, 50, 51, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 75, 76, 77, 78, 80, 81, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 102

Offset: 1

Author

Douglas Latimer, Mar 22 2012

Keywords

• easy
• nonn

Comments

Recall that the nontrivial binomial coefficients are C(n,k), 2 <= k <= n-2.

Examples

			a(1) = 6, since 6 is the lowest nontrivial binomial coefficient.
a(2) = 10, since 10 is the lowest nontrivial binomial coefficient except 6.
a(3) = 12 , since 6 is the lowest nontrivial binomial coefficient and 6+6 = 12 .
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

This is A006987 combined with two-term sums of members of A006987. Cf. A210577 and A007318 .

Programs

Maple

N:= 200: # to get all terms <= N
BC:= {}:
for k from 2 do
   if binomial(k+2,k) > N then break fi;
   for n from k+2 do
     v:= binomial(n,k);
     if v > N then break fi;
     BC:= BC union {v};
   od;
od:
A:= BC:
for i from 1 to nops(BC) do
  A:= A union select(`<=`,map(`+`,BC[1..i],BC[i]),N)
od:
sort(convert(A,list)): # Robert Israel, Apr 27 2017