A133254 Sums of a triangular number A000217 > 0 and a square A000290 > 0.

2, 4, 5, 7, 10, 11, 12, 14, 15, 16, 17, 19, 22, 24, 25, 26, 28, 29, 30, 31, 32, 35, 37, 39, 40, 42, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 61, 64, 65, 67, 70, 71, 72, 74, 75, 77, 79, 80, 81, 82, 84, 85, 87, 91, 92, 94, 95, 96, 100, 101, 102, 103

Offset: 1

Author

Jonathan Vos Post, Dec 19 2007

Keywords

• easy
• nonn

Examples

			a(1) = 2 = 1 + 1 = A000217(1) + A000290(1).
a(2) = 4 = 1 + 3 = A000217(2) + A000290(1).
a(3) = 5 = 1 + 4 = A000217(1) + A000290(2).
a(4) = 7 = 3 + 4 = A000217(2) + A000290(2) = 6 + 1 = A000217(2) + A000290(1).
a(5) = 10 = 1 + 9 = A000217(1) + A000290(3) = 6 + 4 = A000217(3) + A000290(2).
		

Crossrefs

Cf. A000217, A000290.

Programs

Mathematica

With[{nn=70},Take[Union[Flatten[Outer[Plus,Accumulate[Range[nn]],Range[nn]^2]]],nn]] (* Harvey P. Dale, Feb 27 2013 *)

Formula

{a + b such that a is in A000217 and b is in A000290 and a,b > 0}. Sum set of {n^2: n>0} and {n*(n+1)/2: n>0}.

Extensions

Corrected by Harvey P. Dale, Feb 27 2013