A014133 Sum of a square and a triangular number.

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 35, 36, 37, 39, 40, 42, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 61, 64, 65, 66, 67, 70, 71, 72, 74, 75, 77, 78, 79, 80, 81, 82, 84, 85, 87, 91

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A014134 (complement).

Programs

Maple

isA014133 := proc(n)
    local c,t ;
    for c from 0 do
        t := c*(c+1)/2 ;
        if t > n then
            return false;
        end if;
        if issqr(n-t) then
            return true;
        end if;
    end do:
end proc:
for n from 0 to 100 do
    if isA014133(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Oct 11 2014

Mathematica

With[{nn=20},Select[Union[Flatten[Outer[Plus,Range[0,nn]^2,Accumulate[ Range[ 0,nn]]]]], #<=(nn(nn+1))/2&]] (* Harvey P. Dale, Dec 29 2019 *)

Formula

{k: A101428(k) > 0} .- R. J. Mathar, Apr 28 2020