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

1,1

Comments

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

Links

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

Example

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 .

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

Crossrefs

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

Sequence in context: A134616 A362180 A081390 * A274426 A345995 A324456

Adjacent sequences: A210575 A210576 A210577 * A210579 A210580 A210581

Keyword

easy,nonn

Author

Douglas Latimer, Mar 22 2012

Status

approved